Let the probability of success on a Bernoulli trial be 0.20. a. In nine Bernoulli trials, what is the probability that there will be 8 failures? (Round your final answers to 4 decimal places.) Probability b. In nine Bernoulli trials, what is the probability that there will be more than the expected number of failures? (Round your final answers to 4 decimal places.) Probability

1，Suppose you want to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks. The correct alternative hypothesis for this Chi-Square test of Independence is

Select one:

time spent watching TV and time spent reading storybooks are independent.

time spent watching TV and time spent reading storybooks are dependent.

time spent watching TV and time spent reading storybooks have an inverse relationship.

time spent watching TV and time spent reading storybooks are not dependent.

2，

Suppose you want to use a Chi-Square test for independence to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks. The value of the test statistic is given as 13.654 and the critical value as 9.210, then you could conclude that

Select one:

there is a relationship between time spent reading storybooks and time spent watching TV.

more time spent reading storybooks leads to no change in time spent watching TV.

there is no relationship between time spent reading storybooks and time spent watching TV.

more time spent watching TV leads to less time spent reading storybooks.

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6300 and estimated standard deviation σ = 2700. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

-) The probability distribution of x is not normal.

-)The probability distribution of x is approximately normal with μ_x = 6300 and σ_x = 2700.   

-) The probability distribution of x is approximately normal with μ_x = 6300 and σ_x = 1909.19.

-) The probability distribution of x is approximately normal with μ_x = 6300 and σ_x = 1350.00.

What is the probability of x < 3500? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

-) The probabilities increased as n increased.

-) The probabilities decreased as n increased.    

-) The probabilities stayed the same as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia)

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

-It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

-) It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

The mean incubation time of fertilized eggs is 22 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day.

(a) The incubation times that make up the middle 39% of fertilized eggs are ___ to ___ days. (round to the nearest whole number as needed).

Practice problems 1 – Type of variables
1. In the following situations give an example of a parameter and a statistic

a. Political elections
b. Subaru 2020 Forester vehicles c. RUM students
d. Puerto Ricans

2. You are in charge of a local company who wants to obtain mean income of the company’s engineers to compare with the mean income of engineers in the industry. You can either obtain the population mean (parameter) or a sample mean (statistic) to reach a managerial conclusion (both describing the same property, and assume both are feasibly possible to get). Which one would you rather use? Explain

3. Determine the type of variable in the following problems (Nominal, ordinal, quantitative). If quantitative state if it is discrete or continuous

a. Times power outages occur in Mayaguez Terrace last December b. Level of attraction of a person (de feo(a) a guapísimo(a))
c. Volume of chocolate by 25 kids sampled in October.
d. Sustained winds of hurricane Irene in the last 24 hours.

e. Placing at a marathon
f. Cell phone ownership (Yes, No) by citizens who are 50 or older

5. Of the examples above mention one that describes a parameter and one that describes a statistic.

1. It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and indeed they may A, fill to specification, B, underfill, and C, overfill. Generally the practice of underfilling is that which one hopes to avoid. Let P(C) = 0.052 while P(A) = 0.940.

   (a) What is the probability that the box is underfilled, P(B)? (b) Find P(A ∩ B).

   (c) Are A and B mutually exclusive events? Why or why not? (d) Find P(A ∪ B).

   (e) What is the probability that the machine does not overfill?
   (f) What is the probability that the machine either overfills or underfills?

Take a stick of unit length and break it into three pieces, choosing the break point at random. (The break points are assumed to be chosen simultaneously). What is the probability that the three pieces can be used to form a triangle?

Suppose a circular disk is divided into n sectors and that you have ten different colors of paint.

Let Sn denote the number of ways you can paint the n sectors, in a way that no two adjacent sectors are painted the same color.

Formulate a difference equation to determine Sn.

Suppose that Mr. Smith and Mr. James agree to meet at a specified place between 12 pm and 1 pm. Suppose each person arrives between 12 pm and 1 pm at random with uniform probability. What is the distribution function for the length of the time that the first to arrive has to wait for the other

A person has 5 coins in his pocket. Two have both sides being heads, one has both sides being tails, and two are normal. The coins cannot be distinguished unless one looks at them.

a) The person closes his eyes, picks a coin from pocket at random, and tosses it. What is the probability that the down-side of the coin is heads?

b) He opens his eyes and sees that the up-side of the coin is heads. What is the probability that the downside is also heads (namely, this is a two-heads coin).

c) Without looking at the other side of the coin, he tosses it again. What is the probability that the downside is heads?

d) Now he looks at the upside of the coin and it is heads. What is the probability that the downside of the coin is heads?

The maximum temperatures recorded in Houston for the month of January in 2013 are: 67, 46, 56, 50, 47, 60, 57, 64, 67, 69, 73, 75, 72, 45, 42, 52, 63, 62, 68, 69, 71, 71, 75, 79, 79, 78, 77, 81, 77, 61, 67

a. Find Q1, Q2, Q3, the range, and the IQR.

b. Calculate the outlier boundaries for the data set. Are there any outliers?

c. Determine the percentile rank for the 5th order statistic.

Suppose that the national average for the math portion of the College Board's SAT is 513. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 588?

___ %

(b) What percentage of students have an SAT math score greater than 663?

___ %

(c) What percentage of students have an SAT math score between 438 and 513?

___ %

(d) What is the z-score for a student with an SAT math score of 620?

____

(e) What is the z-score for a student with an SAT math score of 405?

____

This is a 3 part question but one question

(A) Discuss the probability of landing on heads if you flipped a coin 10 times?

(B) What is the probability the coin will land on heads on each of the 10 coin flips

(C) Apply this same binomial experiment to a different real-world situation. Describe a situation involving probability.

After analyzing several months of sales data, the owner of an appliance store produced the following joint probability distribution of the number of refrigerators and stoves sold hourly

   0    1 2 Stoves

0    0.08 0.14    0.12    0.34

1    0.09 0.17 0.13    0.39

2    0.05    0.18    0.04 0.27

REF 0.22    0.49    0.29    1

b. What are the laws for a discrete probability density function?

c. If a customer purchases 2 stoves, what is the probability they will also purchase two refrigerators?

d. What is the average number of refrigerators purchased?

e. What is the variance in the number of refrigerators purchased?

f. Are the sale of stores and refrigerators independent?

g. What is the conditional probability distribution for sales in refrigerators if the customer did not purchase a stove?

h. What is the expected value and variance for sales in refrigerators, if the customer did not purchase a stove?

A theme park owner records the number of times the same kids from two separate age groups ride the newest attraction.

Using the computational formula, what is the SS, sample variance, and standard deviation for the age group of 13–16? (Round your answers for variance and standard deviation to two decimal places.)

SS sample variance standard deviation