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Probability Distribution:

Identify Probability Distributions

Determine whether or not a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability disbribution is not given, identify the requiremtns that are not satisfied.

10. Eye Color Groups of five babies are randomly selected. In each group, the random variable x is the number of babies with green eyes (based on data from a study by Dr. Sorita Soni at Indiana University. (The symbol 0+ denotes a positive probability value that is very small)

x P(x)

0 0.528
1 0.360
2 0.098
3 0.013
4 0.001
5 0+

16. Refer to the accompanying table, which describes results from eight offspring peas. The random variable x represents the number of offspring peas with green pods.

x(number of
Peas with
Green Pods) P(x)

0 0+
1 0+
2 0.004
3 0.023
4 0.087
5 0.208
6 0.311
7 0.267
8 0.100

Using probabilities for Unusual Events

a. Find the probability of getting exactly 3 peas with green pods.

b. Find the probability of getting 3 or fewer peas with green pods.

c. Which probability is relevant for determining whether 3 is an unusually low number of peas with green pods:
the result from part (a) or part (b)?

d. Is 3 an unusually low number of peas with green pods? Why or why not?

20. Gender Discrimination - The Telektronic Company hired 8 employees from a large pool of applicants with an equal number of males and females. If the hiring is done without regard to sex, the numbers of females hired and the corresponding probabilities are as follows:

0 (0.004); 1 (0.031); 2 (0.109); 3 (0.219); 4 (0.273); 5 (0.219); 6 (0.109); 7 (0.031); 8 (0.004)

a. Does the given information describe a probability distribution?

b. Assuming that a probability distribution is described, find its mean and standard deviation.

c. Use the range rule of thumb to identify the range of values for usuall numbers of females hired in such groups of eight.

d. If the most recent group of eight newly hired employees does not include any females, does there appear to be discrimination based on sex? Explain.

14. Finding Probabilities When Guessing Answers. A psychology test consists of multiple-choice questions, each having 4 possible answers (a, b, c, d), 1 of which is correct. Assume that you guess the answers to 6 such questions.

a. Use the multiplication rule to find the probability that the first 2 guesses are Wrong and the last 4 guesses are Correct. That is, find P(WWCCCC), where C denotes a correct answer and W denotes a wrong answer.

b. Beginning with WWCCCC, make a complete list of the different possible arrangements of 2 wrong answers and 4 correct answers, then find the probability for each entry in the list.

c. Based on the preceding results, what is the probability of getting exactly 4 correct answers when 6 guesses are made?

32. Credit Rating - There is a 1% delinquency rate for consumers with FICO (Fair Isaac & Company) credit rating scores above 800. If the Jefferson Valley Bank provides large loans to 12 people with FICO scores above 800, what is the probability that at least one of them becomes delinquent? Based on that probability, shoudl the bank plan on dealing with a delinquency?

10. Guessing Answers - The final exam in a sociology course consists of 100 multiple-choice questions. Each question has 5 possible answers, and only 1 of them is correct. An unprepared student makes random guesses for all of the answers.

a. Find the mean and standard deviation for the number of correct answers for such students.

b. Would it be unusual for a student to pass the exam by guessing and getting at least 60 correct answers? Why or why not?

Solution Summary

The solution provides step by step method for the calculation of binomial and normal probabilities. Formula for the calculation and Interpretations of the results are also included.