A) Given a binomial random variable withn= 10 andp= .3, use the formula to find the following probabilities.

a.P(X= 3)

b.P(X= 5)

c.P(X= 8)

B) Given a binomial random variable withn= 6 andp= .2, use the formula to find the following probabilities.

a.P(X= 2)

b.P(X= 3)

c.P(X= 5)

C) A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?

a. One out of the next four cars needs oil

b. Two out of the next eight cars need oil

c. Three out of the next 12 cars need oil

D) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken. What is the probability that 10 or fewer customers chose the leading brand?

E) A certain type of tomato seed germinates 90% of the time. A backyard farmer planted 25 seeds.

a. What is the probability that exactly 20 germinate?

b. What is the probability that 20 or more germinate?

c. What is the probability that 24 or fewer germinate?

d. What is the expected number of seeds that germinate?

F) According to the American Academy of Cosmetic Dentistry, 75% of adults believe that an unattractive smile hurts career success. Suppose that 25 adults are randomly selected. What is the probability that 15 or more of them would agree with the claim?

G) A student majoring in accounting is trying to decide on the number of firms to which he should apply. Given his work experience and grades, he can expect to receive a job offer from 70% of the firms to which he applies. The student decides to apply to only four firms. What is the probability that he receives no job offers?

H) In the United States, voters who are neither Democrat nor Republican are called Independents. It is believed that 10% of all voters are Independents. A survey asked 25 people to identify themselves as Democrat, Republican, or Independent.

a. What is the probability that none of the people are Independent?

b. What is the probability that fewer than five people are Independent?

c. What is the probability that more than two people are Independent?