A car manufacturer crash tests a certain model of car and measures the impact force. The test and model in question produce impact forces that are normally distributed with a mean of 303030 metric tons and a standard deviation of 1.51.51, point, 5 metric tons. Suppose that the manufacturer tests a random sample of 444 cars and calculates the sample mean impact force.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.