Posted: March 2nd, 2017

Would it be unusual for a student to pass by guessing and getting at least 15 correct answers? Why or why not?

Sect. 5-2, p. 209 Identifying Probability Distributions. In Exercise 7-12, determine whether a probability distribution is given. In those cases where a probability distribution is not described, identify the requirements that are not satisfied. In those cases where a probability distribution is described, find its mean and standard deviation. (see example on p. 206, 207)

#7. Genetic Disorder. Three males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the three who inherit the X-linked genetic disorder.
X P(x)
0 0.4219
1 0.4219
2 0.1406
3 0.0156
Answer: µ = σ =

8. Numbers of Girls. A researcher reports that when groups of four children are randomly selected from a population of couples meeting certain criteria, the probability distribution for the number of girls is as given in the accompanying table.

X P(x)
0 0.502
1 0.365
2 0.098
3 0.011
4 0.001
Answer: µ = σ =

10. Mortality Study. For a group of four men, the probability distribution for the number x who live through the next year is as given in the accompanying table.

X P(x)
0 0.0000
1 0.0001
2 0.0006
3 0.0387
4 0.9606
Answer: µ = σ =

#19a,b (see example on p. 209) Expected Value for a Life Insurance Policy. The CNA Insurance Company charges a 21-year old male a premium of $250 for one year $100,000 life insurance policy. A 21-year old male has a 0.9985 probability of living for a year (based on data from the National Center for Health Statistics).
a. From the perspective of a 21-year old male (or his estate), what are the values of the two different outcomes?

Answer:

b. What is the expected value for a 21-year old male who buys the insurance?

Answer:

Sect. 5-3, p. 220 In Exercises 15-20 assume that a procedure yields a binomial distribution with a trial repeated n times. Use Table A-1 to find the probability of x successes given the probability p of success on a given trial.

#19. n = 14, x = 2, p = 0.30

Answer:

20. n = 15, x= 12, p = 0.90

Answer:

#28 [Hint: P(at least 1) = 1 – P(0)] Using Computer Results. In Exercises 25-28, refer to the Minitab display below. The probabilities obtained by entering the values of n = 6 and p = 0.167. In a clinical test of the drug Lipitor, 16.7% of the subjects treated with 10 mg of atorvastatin experienced headaches (based on data from Parke-Davis). In each case, assume that 6 subjects are randomly selected and treated with 10 mg of atorvastatin, then find the indicated probability.

Minitab

Binomial with n = 6 and p = 0.167000
X P(X = x)
0.00 0.3341
1.00 0.4019
2.00 0.2014
3.00 0.0538
4.00 0.0081
5.00 0.0006
6.00 0.0000

Find the probability that at least one subject experiences headaches. Is it unusual to have at least one of six subjects experience headaches?

Answer:

Sect. 5-4, p. 227 Finding u, σ, and Unusual Values. In Exercises 5-8, assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean µ and standard deviation σ. Also, use the range rule of thumb to find the minimum usual value µ – 2σ and the maximum usual value µ + 2
σ.

#7. n = 1492, p = 1/4

10. (For these problems, see examples on p. 225, 226). Guessing Answers. Several economics students are unprepared
for a multiple-choice quiz with 25 questions, and all of their answers are guesses. Each question has five possible answers, and only one of them is correct.
a. Find the mean and standard deviation for the number of correct answers for such students.