Manufacturing and Product Development 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 σ = 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.