Eyedrops are used by many people to soothe and relieve irritation and to lubricate their eyes. A manufacturer claims that the amount of dextran, which helps to prolong the effect of eyedrops, contained in its eyedrops product is 70%. Thirty-six randomly selected bottles of these eye drops were obtained and the sample mean amount of dextran was 68.25%. Assume the population standard deviation is s 5 5%.
a. Find the sampling distribution of the sample mean.
b. Find the probability that the amount of dextran is more than 71%.
c. Does the sample mean found suggest that the manufacturer’s claim is wrong? Justify your answer
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.