5.88 LASIK surgery complications. According to studies, 1% of all patients who undergo laser surgery (i.e., LASIK) to correct their vision have serious post-laser vision problems (All About Vision, 2014). In a random sample of 100,000 LASIK patients, let x be the number who experience serious post-laser vision problems. a. Find E(x). b. Find Var(x). c. Find the z-score for x = 950. d. Find the approximate probability that fewer than 950 patients in a sample of 100,000 will experience serious post-laser vision problems. Find a, b, d

6.38) Cost of unleaded fuel. According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65 (AAA Fuel Gauge Report). Assume that the standard deviation of such costs is $.15. Suppose that a random sample of n = 100 gas stations is selected from the population and the cost per gallon of regular unleaded fuel is determined for each. Consider x, the sample mean cost per gallon. a. Calculate mx and sx. b. What is the approximate probability that the sample has a mean fuel cost between $3.65 and $3.67? c. What is the approximate probability that the sample has a mean fuel cost that exceeds $3.67? d. How would the sampling distribution of x change if the sample size n were doubled from 100 to 200? How do your answers to parts b and c change when the sample size is doubled? Find a, b, c

7.12 The mean and standard deviation of a random sample of n measurements are equal to 33.9 and 3.3, respectively. a. Find a 95% confidence interval for m if n = 100. b. Find a 95% confidence interval for m if n = 400. c. Find the widths of the confidence intervals you calculated in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample

Do parts a and b but find 96.5% (insteadof 95%) confidence intervals.

Using the information in7.60find93%CI and also98.3%CIfor the population proportion of meaningful interactions that were led by children.