math 6

BUSA 2183 Introduction to Business Statistics

Summer 2019 –Session II

Short Exercise 6 (25 points)

IMPORTANT: In any question, if there is a calculation, first provide the formula and then show your calculations for your answers.

Please, provide your answers under each question.

Data files can be found in the D2L.

Question 1 (Short Exercise 2 in the book) (2*2=4 points)

Compute the mean and variance of the following discrete probability distribution.

x	P(x)
2	.5
8	.3
10	.2

a. Mean =

b. Variance=

Question 2 (Short Exercise 10 in the book) (2*3=6 points)

In a binomial situation, n = 5 and π = .40. Determine the probabilities of the following events using the binomial formula.

a. x = 1

b. x = 2

Question 3 (Short Exercise 15 in the book) (2*3=6 points)

Industry standards suggest that 10% of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday.

Data file, “Short Exercise 4_Ch4_15_Question 3”, can be found in the D2L.

a. What is the probability that none of these vehicles requires warranty service?

b. What is the probability exactly one of these vehicles requires warranty service?

c. Compute the mean of this probability distribution and compute standard deviation of this probability distribution.

Question 4 (Short Exercise 20 in the book) (2*2=4 points) Look at the Appendix B for n=12

In a binomial distribution, n = 12 and π = .60. Find the following probabilities.

a. x = 5.

b. x ≤ 5.

Question 5 (Short Exercise 27 in the book) (2.5*2=5 points)

Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans.

a.What is the probability that three loans will be defaulted?

b.What is the probability that at least three loans will be defaulted?