1.Blinko is a game in which three dice are rolled. To win the game, a player mustroll triplesthat is, three of the same number. You roll the dice 20 times.

A.Verify that the situation is binomial.

B.Out of 20 rolls, what is the probability you win exactly 4 times? Show yourwork using the formula for binomial probability. C.What is the probability that you win at least 3 times?(6 points)Note:You may use the calculator to get your answer, but indicate theprocess you used to arrive at it.

D. What is the mean number of wins in 20 rolls of the dice?

2.Jeremy decides to play the game of Blinko and is determined to play until hewins.

A.Is the situation still binomial? Explain.

B.Calculate the probability of getting the first win on the third roll.(4 points)Note: You may use either the formula or the calculator.

C.How many times can he expect to roll the dice in order to win?(4 points)

3. Homeowners' insurance rates vary throughout the country according to a normal distribution with U=600 and a=75. Suppose that FYI Insurance Company decides to conduct a review of 100 of its policies. Upon review of the 100 policies, it is found that the mean annual rate paid is x=625. Assume the100 polices were randomly selected.

A.Calculate the mean and standard deviation of the sampling distribution of x.

B.What does the Central Limit Theorem reveal about the distribution of the sample?

C.What is the probability that the sample mean annual insurance costis greater than $620? Show your work.(6 points)