ques in quantitative tool

a. The mean annual cost of automobile insurance is $939. Assume that the standard 6 deviation is F5245. Required: i. What is the probability that a simple random sample of automobile insurance Page 2 of 5 3/6 policies will have a sample mean within $25 of the population mean for each of the following sample sizes: 30, 50, 100, and 400'? ii. What is the advantage of a larger sample size when attempting to estimate the population mean? I). A simple random sample of size 100 is selected from a population with p:.40. 3 Required: i. What is the expected value of :3? ii. What is the standard error of 35? iii. Show the sampling distribution of 33. e. According to Thomson Financial. the majority of companies reporting prots had beaten 3.5 estimates. A sample of 162 companies showed 104 beat estimates, 29 matched estimates, and 29 fell short. Required: i. What is the point estimate of the proportion that fell short of estimates? ii. Determine the margin of error and provide a 95% condence interval for the proportion that beat estimates. iii. How large a sample is needed if the desired margin of error is .05