1. Let random variable x represent the number of heads when a fair coin is tossed two times.

(a) Construct a table describing the probability distribution.

x | P(X)

0

1

2

(b) Determine the mean and standard deviation of x. Show all work.

2. Mimi plans make a random guess at 10 true-or-false questions. Answer the following questions:

(a) Let X be the number of correct answers 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 she gets at most 5 correct answers. (Round the answer to 3 decimal places.

(c) To get the answers for part (b), what technology did you use? If an online applet was used, list the URL and describe the steps. If a calculator or Excel was used, write out the function.