1. Four coins are tossed 11 times. The number of heads is counted and the following data is reported:
4, 3, 2, 0, 3, 3, 1, 2, 3, 2, 1.
Calculate the following sample statistics. Be sure to provide a formula or an explanation for your answer.
(2) a. Sample mean? (2) d. Sample range?
(2) b. Sample median? (2) e. Sample variance?
(2) c. Sample mode?
2. President Donald Trump has promised to pass a bill to build a wall on the U.S. border. Polls show that 90% of registered Democrats are against this bill, while 60% of registered Republicans and 50% of registered Independents favor the bill. The distribution of party affiliation is 35% Democrat, 30% Republican, and 35% Independent.
(5) a. What is the probability that someone picked at random does not favor the bill?
(5) b. Suppose a randomly selected person does favor the bill. What is the probability that they are registered as a Republican?
3. An urn contains 12 red balls and 8 green balls. Six balls are drawn randomly with replacement.
(3) a. Find the probability of drawing exactly two red balls?
(3) b. Find the probability of drawing at least one green ball?
(4) c. Find the probability of drawing exactly two green balls when the drawings are done without replacement?
4. Let Z be a random variable with the following probabilities.
Z -2 -1 0 1 2
P(Z) .05 .25 .40 .25 .05
(10) a. Calculate the expected value (m) and variance (s2) of Z?
5. Calculate the following probabilities.
(5) a. You draw two cards (w/o replacement) from a standard 52-card deck. What is the probability of drawing exactly one jack?
(5) b. You draw one card from a standard 52-card deck. What is the probability of drawing an ace or a heart?
6. (10) Free Choice Pizza offers many types of pizza toppings. There are 5 types of meats and 6 different vegetables. The super deluxe combo allows you to pick 4 toppings. How many different types of this combo pizza can you order? (Your answer will depend on the assumptions you make about repeating toppings and order of choice)
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