4.

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 significancelevel?

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

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

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

5.

The editor of a book publishing company decides whether to publish a textbook. Before reaching a publishing decision, the book will be reviewed for a positive or negative feedback. In the past, 99% of the huge successes received positive feedbacks, 70% of the moderate successes received positive feedbacks, 40% of the breakeven received positive feedbacks, and 20% of the losers received positive feedbacks. Based on the books published by the company,x%of them are huge successes, 20% of them are moderate successes,y%are breakeven, and 25% are losers.

(a)Giventhattheprobabilityofabookthatreceivesapositivefeedbackis0.469,findx%

andy%.

(b)Based on (a), if the book receives a positive feedback, what is the probability thatitwill be a huge success or a moderatesuccess?

(c)Learning from the past experience, the editor sets up a new rule. For each book that receives negative feedback, there is no chance that the editor will publish it. On the other hand, for each book that receives a positive feedback, there is 80% chance that the editor will publish it. The editor receives 12 reviews and he makes the decision basedoneachfeedbackseparately.Giventhatnomorethan6bookswillbepublished, what is the probability that no less than 3 books will bepublished?