Statistics 2500 Fall 2016, Section 001 Assignment #2 Due date: Wednesday, Nov. 23, 2016 Assignment Requirement: a) The some data sets are available on the course website www.math.mun.ca/~hongwm/S2500. b) Please staple the pages of your assignment together. c) Write your name and student number and lab section number on a cover page of your assignment. d) Drop the completed assignment into the designated Assignment Box on or before the due date. Assignment Questions: 1. A sample of 300 TV viewers were asked to rate the overall quality of television shows from 0 (terrible) to 100 (the best). A histogram was constructed from the results, and it was noted that it was mound-shaped and symmetric, with a sample mean of 65 and a sample standard deviation of 8. Approximately what proportion of ratings would be above 81? 2. A set of final exam grades in ST2500 course is normally distributed with mean 73 and standard deviation of 8. a) What is the probability of getting a grade of 91 or less on this exam? b) What is the probability of that a student scored between 65 and 98? c) The probability is 5% that a student taking the exam scores higher than what grade? 3. The number of loaves of white bread demanded daily at a bakery is normally distributed with mean 7000 loaves and variance 84000. The company decides to produce a sufficient number of loaves so that it will fully supply demand on 90% of all days. a) How many loaves of bread should the company produce? b) Based on (a), on what percentage of days will the company be left with more than 500 loaves of unsold bread? 4. Credit scores are three-digit numbers used by lenders when evaluating your credit worthiness. The scores for residents of 20 metropolitan areas are listed as follows: City Credit Score City Credit Score Atlanta 670 Minneapolis 707 Boston 705 New York 688 Chicago 680 Orlando 671 Cleveland 690 Philadelphia 688 Dallas 653 Phoenix 660 Denver 675 Sacramento 676 Detroit 675 San Francisco 686 Houston 655 Seattle 691 Los Angeles 667 Tampa 675 Miami 672 Washington 693 Refer to the data above and answer the following (you can obtain the data for R on the course website. You may the data is by clicking the file name here creditscore.txt). 1 a) b) c) Construct a histogram of the credit scores. Do the credit scores appear approximately normally distributed? Explain. Construct a normal probability plot (QQ-plot) of the credit scores. Do the credit scores appear approximately normally distributed? Explain. If your answer in (b) is yes, find the probability that a city will have a credit score of at least 680. Use the sample mean of the data for , and the sample standard deviation for . 5. An article in the New York Times reported that the mean download time for the H & R Block website was 2.5 seconds. Suppose we also know that 93% of the downloads can be done in less than 3 seconds. If we assume the download times are normally distributed, what is the standard deviation? 6. Time spent using email per session is normally distributed with = 8 minutes and = 2 minutes. If you select random sample of 25 sessions, a) What is the probability that the sample mean is between 7.8 and 8.2 minutes? b) What is the probability that the sample mean is between 7.5 and 8.0 minutes? c) If you select random sample of 100 sessions, what is the probability that the sample mean is between 7.8 and 8.2 minutes? d) Explain the difference in the results of a) and c). 7. The Canada Revenue Agency announced that it planned to resume totally random audits in 2004. Suppose that you select a random sample of 200 totally random audits, and that only 10% of all the returns filed would result in audits requiring additional taxes. Verify the normal approximation to the binomial distribution can be applied here and find the probabilities that the sample has a) At least 89% but at most 91% no-change audits? b) At least 85% but at most 95% no-change audits? c) More than 95% no-change audits? 8. The mean of the annual return for common stocks from 1926 to 1992 was 12.4 percent with a standard deviation of 20.6 percent. What is the probability that the average return rate for a random sample of 53 common stocks was: a) less than 19 percent? b) between 21 and 22.4 percent? 9. The data in bankcosti.txt represent some bank data including the bounced check fee in dollars for a sample of 23 banks for direct-deposit customers who maintained a $100 balance. a) Construct a 95% confidence interval for the population mean bounced check fee; b) Construct a 98% confidence interval for the population mean bounced check fee; c) What assumption did you have to make to construct the confidence intervals above? d) Construct appropriate plots to evaluate the assumption made in c). Explain whether the assumption appears valid. 2