### The number of components produced per hour is normally distributed with a mean of 25 and a standard deviation of 4.

- 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?

- 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).
- 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.
- 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?

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