Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $20 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 70 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μ_x = 20 and standard error σ_x = $0.84.The sampling distribution of x is approximately normal with mean μ_x = 20 and standard error σ_x = $0.10.    The sampling distribution of x is not normal.The sampling distribution of x is approximately normal with mean μ_x = 20 and standard error σ_x = $7.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is necessary to assume that x has an approximately normal distribution.It is not necessary to make any assumption about the x distribution because n is large.    It is necessary to assume that x has a large distribution.It is not necessary to make any assumption about the x distribution because μ is large.

(b) What is the probability that x is between $18 and $22? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $18 and $22? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 70 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The sample size is smaller for the x distribution than it is for the x distribution.The standard deviation is larger for the x distribution than it is for the x distribution.    The x distribution is approximately normal while the x distribution is not normal.The standard deviation is smaller for the x distribution than it is for the x distribution.The mean is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $38 and the estimated standard deviation is about $5.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is not necessary to make any assumption about the x distribution because n is large.It is necessary to assume that x has an approximately normal distribution.    It is necessary to assume that x has a large distribution.It is not necessary to make any assumption about the x distribution because μ is large.

(b) What is the probability that x is between $36 and $40? (Round your answer to four decimal places.)

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $36 and $40? (Round your answer to four decimal places.)

(d) In part (b), we used x, the average amount spent, computed for 40 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The mean is larger for the x distribution than it is for the x distribution.The sample size is smaller for the x distribution than it is for the x distribution.    The standard deviation is smaller for the x distribution than it is for the x distribution.The standard deviation is larger for the x distribution than it is for the x distribution.The x distribution is approximately normal while the x distribution is not normal.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.    

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $16 and the estimated standard deviation is about $9. (a) Consider a random sample of n = 130 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? The sampling distribution of x is not normal. The sampling distribution of x is approximately normal with mean μx = 16 and standard error σx = $0.07. The sampling distribution of x is approximately normal with mean μx = 16 and standard error σx = $0.79. The sampling distribution of x is approximately normal with mean μx = 16 and standard error σx = $9. Is it necessary to make any assumption about the x distribution? Explain your answer. It is not necessary to make any assumption about the x distribution because n is large. It is necessary to assume that x has an approximately normal distribution. It is necessary to assume that x has a large distribution. It is not necessary to make any assumption about the x distribution because μ is large. (b) What is the probability that x is between $14 and $18? (Round your answer to four decimal places.) (c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $14 and $18? (Round your answer to four decimal places.) (d) In part (b), we used x, the average amount spent, computed for 130 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen? The standard deviation is smaller for the x distribution than it is for the x distribution. The x distribution is approximately normal while the x distribution is not normal. The standard deviation is larger for the x distribution than it is for the x distribution. The mean is larger for the x distribution than it is for the x distribution. The sample size is smaller for the x distribution than it is for the x distribution. In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer? The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer. The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.

1. Determining Inheritance using Punnett Squares

A Punnett is a means to determine the genetic inheritance of offspring if the genotypes of both parents are known. Using Punnett squares answer the questions about the following scenarios. In order to properly answer some of the questions more than 1 Punnett square might be needed. With every Punnett square provide a key for your alleles.

1. Neurofibromatosis (NF), sometimes called von Recklinghausen disease, is one of the most common genetic disorders. It affects roughly 1 in 3,000 people. It is seen equally in every racial and ethnic group throughout the world. At birth or later, the affected individual may have six or more large tan spots on the skin. Such spots may increase in size and number and become darker. Small benign tumors called neurofibromas may occur under the skin or in the muscles. They are made up of nerve cells and other cell types. NF is a dominant disorder. Jane has NF and wants to figure out what the chances are that her children will inherit the disorder if her husband, John, does not have NF.

2. The condition of sickle cell anemia is recessive and only the homozygous recessive individuals are adversely affected. Interestingly, heterozygous individuals have increased resistance to Malaria which is caused by a Plasmodium parasite that infects red blood cells. A heterozygous individual has red blood cells that are minimally affected but are altered enough so that Plasmodium cannot infect the cells. This is one reason why this allele persists in the population – in the heterozygous state it gives the individual an advantage for survival in some environments.

Veronica, who has the sickle cell condition, and Mason who does not have the condition have a child. They are worried about the having a child with sickle cell anemia and malaria because they are moving to a part of Africa where the Plasmodium is common. Who in this family should be worried about sickle cell anemia and contracting malaria?

3. All newborn babies are tested to see if they have a defective enzyme which cannot break down the amino acid phenylalanine. If phenylalanine accumulates in the blood then high levels can cause mental retardation. The condition is called phenylketonuria or PKU. PKU is a recessive allele and only homozygous recessive individuals are affected. A family living in a country where PKU testing is not done wanted to know if they should have their baby in the US. The pregnant mother has a parent who has the PKU condition and the father also has one parent with the condition. Neither the pregnant mother nor the father has the condition. Draw a punnett square demonstrating the likelihood that this new baby will inherit PKU and discuss why or why not the parents should have the baby in the US. (K = dominant, non-disease allele; k = recessive, disease allele)
4. Huntington’s disorder is caused by a dominant allele. Heterozygous individuals with one copy of this allele suffer from progressive degeneration of the nervous system and premature death. The phenotype or symptoms do not appear until the affected individual reaches ~40 years of age. This is after child-bearing age, so people have children before they know they are carrying the affected gene allele.

Jermaine is very worried about passing the dominant Huntington’s gene allele to his children. If Jermaine’s father has the Huntington’s Disorder, his mother does not, and his wife has no history of Huntington’s, does Jermaine need to be tested for Huntington’s before he has children? Note: homozygous dominant is lethal and a fetus will not survive. Draw a punnett square representing the Jermaine’s father and mother, to determine his chances of carrying the Huntington’s disease allele. (H = dominant, disease allele; h = recessive, non-disease allele)

What is the probability that Jermaine has the Huntington’s disease allele? Should he be tested?

If Jermaine is positive for the Huntington’s allele, what are the chances he will pass it on to his children? Do a second punnett square to illustrate this cross.

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $38 and the estimated standard deviation is about $5.

(a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μ_x = 38 and standard error σ_x = $5.The sampling distribution of x is approximately normal with mean μ_x = 38 and standard error σ_x = $0.13.    The sampling distribution of x is approximately normal with mean μ_x = 38 and standard error σ_x = $0.79.The sampling distribution of x is not normal.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is not necessary to make any assumption about the x distribution because n is large.It is necessary to assume that x has an approximately normal distribution.    It is necessary to assume that x has a large distribution.It is not necessary to make any assumption about the x distribution because μ is large.

(b) What is the probability that x is between $36 and $40? (Round your answer to four decimal places.)

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $36 and $40? (Round your answer to four decimal places.)

(d) In part (b), we used x, the average amount spent, computed for 40 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The mean is larger for the x distribution than it is for the x distribution.The sample size is smaller for the x distribution than it is for the x distribution.    The standard deviation is smaller for the x distribution than it is for the x distribution.The standard deviation is larger for the x distribution than it is for the x distribution.The x distribution is approximately normal while the x distribution is not normal.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.    

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $10 and the estimated standard deviation is about $9.

(a) Consider a random sample of n = 100 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is not normal.The sampling distribution of x is approximately normal with mean μ_x = 10 and standard error σ_x = $9.     The sampling distribution of x is approximately normal with mean μ_x = 10 and standard error σ_x = $0.09.The sampling distribution of x is approximately normal with mean μ_x = 10 and standard error σ_x = $0.90.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is necessary to assume that x has an approximately normal distribution.It is not necessary to make any assumption about the x distribution because n is large.     It is necessary to assume that x has a large distribution.It is not necessary to make any assumption about the x distribution because μ is large.

(b) What is the probability that x is between $8 and $12? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $8 and $12? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 100 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The standard deviation is larger for the x distribution than it is for the x distribution.The standard deviation is smaller for the x distribution than it is for the x distribution.     The sample size is smaller for the x distribution than it is for the x distribution.The mean is larger for the x distribution than it is for the x distribution.The x distribution is approximately normal while the x distribution is not normal.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.    

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $25 and the estimated standard deviation is about $8.

(a) Consider a random sample of n = 100 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μ_x = 25 and standard error σ_x = $8. The sampling distribution of x is approximately normal with mean μ_x = 25 and standard error σ_x = $0.08.     The sampling distribution of x is not normal. The sampling distribution of x is approximately normal with mean μ_x = 25 and standard error σ_x = $0.80.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is necessary to assume that x has a large distribution. It is not necessary to make any assumption about the x distribution because μ is large.     It is necessary to assume that x has an approximately normal distribution. It is not necessary to make any assumption about the x distribution because n is large.

(b) What is the probability that x is between $23 and $27? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $23 and $27? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 100 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The standard deviation is larger for the x distribution than it is for the x distribution. The sample size is smaller for the x distribution than it is for the x distribution.     The standard deviation is smaller for the x distribution than it is for the x distribution. The x distribution is approximately normal while the x distribution is not normal. The mean is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer. The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $46 and the estimated standard deviation is about $9. (a) Consider a random sample of n = 80 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? The sampling distribution of x is not normal. The sampling distribution of x is approximately normal with mean μx = 46 and standard error σx = $9. The sampling distribution of x is approximately normal with mean μx = 46 and standard error σx = $1.01. The sampling distribution of x is approximately normal with mean μx = 46 and standard error σx = $0.11. Is it necessary to make any assumption about the x distribution? Explain your answer. It is necessary to assume that x has an approximately normal distribution. It is not necessary to make any assumption about the x distribution because n is large. It is necessary to assume that x has a large distribution. It is not necessary to make any assumption about the x distribution because μ is large. (b) What is the probability that x is between $44 and $48? (Round your answer to four decimal places.) (c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $44 and $48? (Round your answer to four decimal places.) (d) In part (b), we used x, the average amount spent, computed for 80 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen? The x distribution is approximately normal while the x distribution is not normal. The standard deviation is larger for the x distribution than it is for the x distribution. The standard deviation is smaller for the x distribution than it is for the x distribution. The mean is larger for the x distribution than it is for the x distribution. The sample size is smaller for the x distribution than it is for the x distribution. In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer? The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer. The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $34 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 50 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the xdistribution?

The sampling distribution of x is approximately normal with mean μ_x = 34 and standard error σ_x = $0.99.The sampling distribution of x is approximately normal with mean μ_x = 34 and standard error σ_x = $7.     The sampling distribution of x is approximately normal with mean μ_x = 34 and standard error σ_x = $0.14.The sampling distribution of x is not normal.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is not necessary to make any assumption about the x distribution because n is large.It is not necessary to make any assumption about the x distribution because μ is large.     It is necessary to assume that x has a large distribution.It is necessary to assume that x has an approximately normal distribution.

(b) What is the probability that x is between $32 and $36? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $32 and $36? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 50 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The standard deviation is larger for the x distribution than it is for the x distribution.The x distribution is approximately normal while the x distribution is not normal.     The standard deviation is smaller for the x distribution than it is for the x distribution.The sample size is smaller for the x distribution than it is for the x distribution.The mean is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.     

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $19 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μx = 19 and standard error σx = $1.11.

The sampling distribution of x is approximately normal with mean μx = 19 and standard error σx = $7.

The sampling distribution of x is approximately normal with mean μx = 19 and standard error σx = $0.18.

The sampling distribution of x is not normal.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is not necessary to make any assumption about the x distribution because n is large.

It is necessary to assume that x has a large distribution.

It is not necessary to make any assumption about the x distribution because μ is large.

It is necessary to assume that x has an approximately normal distribution.

(b) What is the probability that x is between $17 and $21? (Round your answer to four decimal places.)

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $17 and $21? (Round your answer to four decimal places.)

(d) In part (b), we used x, the average amount spent, computed for 40 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The mean is larger for the x distribution than it is for the x distribution.

The standard deviation is smaller for the x distribution than it is for the x distribution.

The x distribution is approximately normal while the x distribution is not normal.

The sample size is smaller for the x distribution than it is for the x distribution.

The standard deviation is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.

The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.