In a factory, one worker produces an average of 175 units per day with a standard deviation of 20. Another worker produces at an average rate of 165 per day with a standard deviation of 21. What is the probability that the production of worker 1 will be larger than that of worker 2 by more than 400 units during 50 working days?

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Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed. A random sample of 15 teenagers was drawn and each reported the amount of time spent at part-time jobs (in minutes).

These are listed here. 180 130 150 165 90 130 120 60 200 180 80 240 210 150 125

(a) Given that the margin of error for the population mean is 27.7064, determine the corresponding critical value. What is the associated significance level?

(b) Based on (a), determine the associated confidence interval estimate of the population mean. State clearly the level of confidence in this problem.

(c) Determine the 90% confidence interval estimate of the population variance.

(d) Give an interpretation for the confidence intervals in (b) and (c).