The manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new component. A random sample of 64 workers indicates a mean time of 16.2 minutes. Assume that the population standard deviation of this assembly time is known to be 3.6 minutes.

a)(5 marks)Construct a 95% confidence interval for the mean assembly time.

b)(4 marks)

How many workers should be involved in this study in order to have the mean assembly time estimated within 0.5 minutes of the population mean with 97.5% confidence

c)Which of the following is a property of the sampling distribution of the sample mean, x? Clearly circle one response only.

A. If you increase your sample size, the sample mean, x, will always get closer to the population mean, .

B. The standard deviation of the sample mean is generally larger than the standard deviation from the original population, .

C. The mean of the sampling distribution of x is

, the population mean.

D. The sampling error will account, in part, for errors that occur in the collection, recording and tabulation of the dat