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1.Find the critical value zc necessary to form a confidence interval at the given level of confidence. a.90% b.97% a) zc = 1.645 b) zc = 2.17 2.A group of 40 bowlers showed that their average score was 192. The population standard deviation is known to be 8. a.Find the margin of error E for a 95% confidence interval. Round your answer to the nearest tenths. b.Construct a 95% confidence interval for the mean score, ? of all bowlers. a) Margin of error, E = zc*σ/√n = 1.96*8/√40 = 2.479 = 2.5 b) A 95% confidence interval for the mean score is given by (Xbar – E, Xbar + E) = (192 – 2.5, 192 + 2.5) = (189.5, 194.5) 3. In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true average time is within 15 minutes of the sample average? Assume the standard deviation of all times is 30 minutes. The required sample size, n = (zc*σ/E)2 = (2.576*30/15)² = 26.54 = 27 4. In a random sample of 26 computers, the mean repair cost was $130 with a sample standard deviation of $36. Assume that the population is normally distributed a.Find the margin of error for a 95% confidence interval. b.Find a 95% co Since the population standard deviation is unknown, a Student’s t distribution with (n-1) = (26-1) = 25 degrees of freedom is used to construct the confidence interval. The critical value tc at a 95% confidence is 2.06 a) Margin of error, E = tc*s/√n = 2.06*36/√26 = 14.54 b) A 95% confidence interval for the mean repair cost is given by (Xbar – E, Xbar + E) = (130 – 14.54, 130 + 14.54) = ($115.46, $144.54)