Question 1- Let random variable x represent the number of heads when a fair coin is tossed three times. Show all work. Just the answer, without supporting work, will receive no credit.
a. Construct a table describing the probability distribution.
b. Determine the mean and standard deviation of x. (Round the answer to two decimal places).
Question 2- Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 10 times.
a. Let X be the number of returns that Mimi gets. As we know, 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), respectively?
b. Find the probability that that she returns at least 1 of the 10 serves from her opponent.