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