1. A bowl of Halloween candy contains 20 KitKats and 35 Snickers. You are getting ready to grab 2 pieces of candy from the bowl without looking. Create a probability distribution where the random variable, x, represents the number of Snickers picked. (You can treat the probabilities as with replacement).
In: Math
The distribution of actual weights of 8-oz chocolate bars produced by a certain machine is normal with mean 7.8 ounces and standard deviation 0.2 ounces. (a) What is the probability that the average weight of a bar in a random sample with three of these chocolate bars is between 7.64 and 7.96 ounces?
ANSWER:
(b) For a random sample of three of these chocolate bars, what is the level L such that there is a 4% chance that the average weight is less than L?
ANSWER:
Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean 129 mg/dl and standard deviation 8 mg/dl. Let LL denote a patient's glucose level.
(a) If measurements are made on three different days, find the
level LL such that there is probability only 0.05 that the mean
glucose level of three test results falls above LL for Shelia's
glucose level distribution. What is the value of LL?
ANSWER:
(b) If the mean result from the three tests is compared to the
criterion 140 mg/dl, what is the probability that Shelia is
diagnosed as having gestational diabetes?
ANSWER:
The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=559.2μ=559.2 and standard deviation σ=28σ=28.
(a) What is the probability that a single student randomly
chosen from all those taking the test scores 563 or higher?
ANSWER:
For parts (b) through (d), consider a random sample of 25 students
who took the test.
(b) What are the mean and standard deviation of the sample mean
score x¯x¯, of 25 students?
The mean of the sampling distribution for x¯x¯
is:
The standard deviation of the sampling distribution for x¯x¯
is:
(c) What z-score corresponds to the mean score x¯x¯ of
563?
ANSWER:
(d) What is the probability that the mean score x¯x¯ of these
students is 563 or higher?
ANSWER:
In: Math
The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores on the quantitative portion of the GRE follow a normal distribution with standard deviation of 8.8. Suppose a random sample of 10 students took the test, and their scores are given below:
152, 126, 146, 149, 152, 164, 139, 134, 145, 136
PLEASE TYPE DONT WRITE THANK YOU!!
In: Math
PLEASE SHOW ALL WORK IN EXCEL.
Use Bilingual sheet to answer this question.
A national survey of companies included a question that asked whether the company had at least one bilingual telephone operator. The sample results of 90 companies follow (Y denotes that the company does have at least one bilingual operator; N denotes that it does not).
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The file Dataset_HW-3, sheet named Bilingual also contains the above survey results. Use this information to estimate with 80% confidence the proportion of the population that does have at least one bilingual operator.
[3 points]
Use Part-2 sheet to answer this question.
You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the amount a family has spent on food during a year has been approximately $1000. If you want to be 99% sure that you have estimated average family food expenditures within $50, how many families do you need to survey?
[2.5 points]
Use Part-3 sheet to answer this question.
You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value? [Hint: proportion est. = 0.5]
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In: Math
Records over the past year show that 1 out of 300 loans made by Mammon Bank have defaulted. Find the probability that 5or more out of 320 loans will default. Hint: Is it appropriate to use the Poisson approximation to the binomial distribution? (Round λ to 1 decimal place. Use 4 decimal places for your answer.)
In: Math
Wild fruit flies have red eyes. A recessive mutation produces white-eyed individuals. A researcher wants to assess the proportion of heterozygous individuals. A heterozygous red-eyed fly can be identified through its off-spring. When crossed with a white-eyed fly it will have a mixed progeny.
A random sample of 100 red-eyed fruit flies was taken. Each was crossed with a white- eyed fly. Of the sample flies, 12 were shown to be heterozygous because they produced mixed progeny.
a) Check this data for the conditions necessary for the calculation of a large-sample confidence interval. Does it comply OR should you use the plus-four interval only?
b) Calculate the summary statistics from these data.
c) Determine a 95% confidence interval for the proportion of heterozygous flies.
d) Also use a test of significance at the 5% level to test the hypothesis that the proportion of heterozygous red-eyed flies is different to a proposed theoretical value of 17%?
e) Compare the answer from this test at the 5% level in d) to the conclusion you could make from the 95% confidence interval in c). Would you necessarily expect the same answer?
In: Math
CASE STUDY CH.6
DROPBOX ASSIGNMENT
A spice manufacturer has a machine that fills bottles. The bottles are labeled 16 grams net weight so the company wants to have that much spice in each bottle. The company knows that just like any packaging process this packaging process is not perfect and that there will some variation in the amount filled. If the machine is set at exactly 16 grams and the normal distribution applies, then about half of the bottles will be underweight making the company vulnerable to bad publicity and potential lawsuits. To prevent underweight bottles, the manufacturer has set the mean a little higher than 16 grams. Based on their experience with the packaging machine, the company believes that the amount of spice in the bottle fits a normal distribution with a standard deviation of 0.2 grams. The company decides to set the machine to put an average 16.3 grams of spice in each bottle. Based on the above information answer the following questions:
1) What percentage of the bottles will be underweight? (5 Points)
2) The company's lawyers says that the answer obtained in question 1 is too high. They insist that no more then 4% of the bottles can be underweight and the company needs to put a little more spice in each bottle. What mean setting do they need? (5 Points)
3) The company CEO says that they do not want to give away too much free spice. She insists that the machine be set no higher than 16.2 grams (for the average) and still have only 4% underweight bottles as specified by the lawyers. This can be only accomplished by reducing the standard deviation. What standard deviation must the company achieve to meet the mandate from the CEO? (4 Points)
4) A disgruntled employee decides to set the machine to put an average 17.4 grams of spice in each bottle. What % of the bottles will be over weight (use standard deviation of 0.2 grams for this question)? (5 Points Hint: this question is similar to Question 1 but make sure you draw a diagram so as to answer this question correctly)
5) Can you think of a practical way as to how the company can reduce the standard deviation for this bottle filling process? (1 Point)
In: Math
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be 80% confident that his estimate is within seven percentage points of the true population percentage? Complete parts (a) through (c) below
a) Assume that nothing is known about the percentage of adults who have heard of the brand.
n=
(Round up to the nearest integer.)
b) Assume that a recent survey suggests that about 86% of adults have heard of the brand.
n=
(Round up to the nearest integer.)
In: Math
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,300. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)
(a) Find the 90th percentile for an individual teacher's salary.
(b) Find the 90th percentile for the average teacher's salary.
A typical adult has an average IQ score of 105 with a standard deviation of 20. If 19 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 123 points? (Round your answer to five decimal places.)
In: Math
Define 2 different measures of correlation of 2 data sets to each other.
In: Math
List all basic distributions for which:
a) MLE is unbiased, but Method of Moments (MM) estimator is biased
b) MLE is biased, but MM estimator is unbiased
In: Math
An industrial plant discharges water into a river. An environmental protection agency has studied the discharged water and found the lead concentration in the water (in micrograms per litre) has a normal distribution with population standard deviation σ = 0.7 μg/l. The industrial plant claims that the mean value of the lead concentration is 2.0 μg/l. However, the environmental protection agency took 10 water samples and found that the mean is 2.56 μg/l. A hypothesis test is carried out to determine whether the lead concentration population mean is higher than the industrial plant claims. (Use 1% level of significance). An appropriate test for this one population hypothesis problem is to use the _______.
In: Math
A random sample of 20 observations results in 11 successes.
[You may find it useful to reference the z
table.]
a. Construct the an 90% confidence interval for
the population proportion of successes. (Round intermediate
calculations to at least 4 decimal places. Round "z" value
and final answers to 3 decimal places.)
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Construct the an 90% confidence interval for the population proportion of failures. (Round intermediate calculations to at least 4 decimal places. Round "z" value and final answers to 3 decimal places.)
|
In: Math
Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approval process is too easy and, as a result, too many drugs are approved that are later found to be pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe.
In: Math
One state lottery game has contestants select 5 different numbers from 1 to 45. The prize, if all numbers are matched is 2 million dollars. The tickets are $2 each.
1) How many different ticket possibilities are there?
2) If a person purchases one ticket, what is the probability of winning? What is the probability of losing?
3) Occasionally, you will hear of a group of people going in together to purchase a large amount of tickets. Suppose a group of 30 purchases 6,000 tickets. a) How much would each person have to contribute? b) What is the probability of the group winning? Losing?
4) How much would it cost to “buy the lottery”, that is, buy a ticket to cover every possibility? Is it worth it?
5) Create a probability distribution table for the random variable x = the amount won/lost when purchasing one ticket.
6) In fair games, the expected value will be $0. This means that if the game is played many…many times, then one is expected to break even eventually. This is never true for Casino and Lottery games. Find the expected value of x = the amount won/lost when purchasing one ticket.
7) Interpret the expected value. See section 4.2 in the textbook for an example on how to interpret the expected value.
8) Fill in the following table using the expected value.
| Number of tickets purchases | Expected net winnings for the lottery | Expected net winnings of a fair game (expected value = 0) |
| 100,000 | $0 | |
| 500,000 | $0 | |
| 1,000,000 | $0 | |
| 5,000,000 | $0 |
Please answer all questions! I will rate you!
In: Math