Individuals who belong to a health maintenance organization (HMO) usually share the cost of certain medical services, for example, paying $10 for an office visit. An insurance company study indicates that the proportion of all people who belong to an HMO who have a copayment of more than $10 for an office visit is 0.65. Suppose 1000 people who belong to an HMO are randomly selected, and the office copayment amount is recorded.
a. Find the distribution of the sample proportion of people who have a copayment of more than $10 for an office visit. Verify the nonskewness criterion.
b. Find the probability that the sample proportion is more than 0.66.
c. Find the probability that the sample proportion is between 0.64 and 0.67.
d. Find a value h such that the probability that the sample proportion is less than h is 0.01.
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