In a job shop there are five lathes which produce automotive components. The number of components produced per hour is normally distributed with a mean of 25 and a standard deviation of 4

1)In a job shop there are five lathes which produce automotive components. The number of components produced per hour is normally distributed with a mean of 25 and a standard deviation of 4. 

a) What percentage of the time does a lathe produce more than 27 components per hour?

b) What percentage of the time is the average rate of output of the five lathes more than 27 components per hour?

2)The manager of an EZ lube service station has reduced an oil-change job to a science and wants to keep it that way. The manager constantly monitors the performance of his staff. This week, 15 oil-change jobs were sampled with a sample mean of 9.8 minutes per job. Experience has shown that the times follow a normal distribution, and the standard deviation of the population is known to be 1.2 minutes. Based on this week’s sample, construct a 90% confidence interval for the population mean (average time for an oil-change job). 

3)An apartment-finder service would like to estimate the average cost of a one-bedroom apartment in Denton, Texas. A random sample of 41 apartment complexes yielded a mean of $310 with a standard deviation of $29. Construct a 90% confidence interval for the mean cost of one-bedroom apartments in Denton, Texas. 

4)A bank manager would like to estimate the mean deposit by a customer into a savings account to within $500. If the deposits into savings accounts are considered to be normally distributed with a standard deviation of $1,250, what sample size would be necessary at a 90% confidence level to determine the same?