Suppose X is a random variable with probability distribution given by
a. Find the mean, variance, and standard deviation of X.
b. Suppose p(x) 5 1/6, x 5 1, 2, 3, 4, 5, 6. Find the mean, variance, and standard deviation of X.
c. Suppose p(x) 5 1/n, x 5 1, 2, 3, c, n. Find the mean, variance, and standard deviation of X in terms of n.
According to a Pew Research Center survey, approximately 35% of Americans attempt to diagnose a medical condition online.49 Highmark insurance company is concerned about the rising number of online diagnosers and the resulting failure to consult a physician. They have decided to select 25 policyholders at random. If the number of online diagnosers is 11 or fewer, then no action will be taken. Otherwise, they will begin a campaign to remind policyholders that they should always consult a physician to confirm a medical condition.
a. Suppose the true proportion of online diagnosers is 0.35. What is the probability that Highmark will begin a new reminder campaign?
b. Suppose the true proportion of online diagnosers is 0.40. What is the probability that no action will be taken? What if the true proportion is 0.50?
c. Suppose the decision rule is changed such that if the number of online diagnosers is 12 or fewer, then no action will be taken. Answer parts (a) and (b) using this rule.