Question

Efficient manufacturing: Efficiency experts study the processes used to manufacture items i order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 55 clamps, the mean time to complete this step was 50.0 seconds. Assume that the population standard deviation is o = 8 seconds. Part 1 Construct a 99% confidence interval for the mean time needed to complete this step. Round to one decimal place, if necessary. A 99% confidence interval for the mean is (17.2 << 52.8. Part 2 out of 2 Find the sample size needed so that a 95% confidence interval will have margin of error of 1.5. (Round the critical value to no less than three decimal places.) A sample size of h error of 1.5. i s needed in order to obtain a 95% confidence interval with a margin

Answer 1

solution - Given that & Sample ) 355 mean (u) = 500 CD =8 * Part -2 we find qui cf for the mean time needed 997. z critical Value 21, = 2.58 V55 50.0+ 2.58x-2 50.01 258x8 - 7.416 = 50.032.58x1-07-87 - 50.01 2-7831 - 50.072-7831, 50-2.483 = (52.78, 47.2169) A 991. confidence interval for the mean is 47.21<4<152.31 part a out of a we find 95%. I margin of error of 1.5 95% CI Z critical vame zon = 1.96 E -15 Sample slike na fam sample siate n=1 ] 1-4687

. = (10.453332 109.272 H o A sample gite of (109) is needs in order to obtain a 95%. interval with a margin of error of 1.5. confidence