1) It appears that new car purchases have peaked in 2018 vs. used car purchases. The following probability distribution table shows the random variable x, where x is the number of new cars purchased by household during the last five years:

x       P(x)

0        0.15

1        0.25

2        0.45

3        0.14

4        0.01

a. What is the mean of x (round to 2 decimal places)

b. What is the standard deviation of x

2. In a Sunday baseball league, Mike Kulansky had a 0.500 probability of hitting safely. Assume he had 8 bats in one game.

a. Let X be the number of hits Mike got. The distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q).

b. Find the probability that he gets at least 5 hits in one game (round to 3 decimals)

3. Assume that gas mileage for cars is normally distributed with a mean of 25 miles per gallon and a standard deviation of 10 miles per gallon.

a. What is the probability that a randomly selected car gets between 22 and 28 miles per gallon? (round to 4 decimals)

b. Find the 90th percentile of the miles per gallon distribution (round to 2 decimals)

4. A psychologist is evaluating different therapies for treating depression. The psychologist selects 100 clients and randomly assigns 25 to each group. After 8 weeks of treatment a depression inventory is administered. Which statistical approach should be used?

a. confidence interval

b. t-test

c. ANOVA

d. Chi square