MATH 1F92 - Assignment # 5 Due: Friday, November 27, 2015 by 11:00 AM Assignments must have a cover page (refer to the course outline). Please write on one side of the page only and show ALL your work. Answer questions with sentences. Include any printout for a question with the question and clearly label the printout with the question number and part. Keep three decimal places. Please read Sections 7.1, 7.2, and 7.3 the textbook. 1. The amount of time spent waiting in line at a grocery store express checkout varies from 5 minutes to 15 minutes and follows a uniform distribution. Let X be the amount of time spent waiting in line. a) Draw a sketch of the distribution of X. b) Find the probability that a customer waits in line for at most 7 minutes. c) Find the probability that a customer waits for more than 12 minutes. d) Find the probability that a customer waits between 6 minutes and 13 minutes. e) Find the probability that a customer waits exactly 8 minutes. f) Suppose you arrive at the express checkout (with less than 8 items, of course) at 5:00 p.m. and have plans to meet a friend at the food court at 5:20 p.m. If it takes 6 minutes for your groceries to be scanned and paid for and 2 minutes to walk from the store to the food court, what is the probability you will be on time to meet your friend? 2. Heights of women are normally distributed with a mean of 63.5 inches and a standard deviation of 2.5 inches. Draw a sketch of the distribution of women's heights, labelling , , 2 and 3 on your sketch. Use this information and the Empirical Rule to answer a) to d), shading the areas that represent the percentages/probabilities you have found. a) Approximately what percentage of women is taller than 71 inches? b) What is the approximate probability that a randomly selected woman is between 56 and 58.5 inches tall? c) What is the maximum possible height of a woman who falls within the shortest 2.5% of all women? d) In a group of 1000 women, approximately how many would you expect to be between 58.5 and 66 inches tall? e) Excel We generate a random sample of heights of 1000 women following the steps below: In A1, enter the following function: =rand() In B1, enter the following function =normsinv(A1) In C1, enter the following function: =$E$1+B1*$F$1 In E1, type in 63.5 Page 1 of 3 In F1, type in 2.5 Select data range A1 to C1. Use fill handle to copy down the formula to row 1000 Obtain a histogram and descriptive statistics for the heights of the 1000 women sampled. Attach your Excel output here. f) Describe the distribution of sample heights. Compare the shape, centre and spread to those of the theoretical model. 3. (a) If the area to the right of z is 0.8907, what is z from table V? (b) Write down the formula in Excel to find z in part (a) (c) Find the area of the shaded region z= - 0.84 z=1.28 (d) Write down the Excel formula for (c). 4. The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 8.8. (Source: http://www.ets.org/.) A graduate school requires that students score above 160 to be admitted. a. What proportion of combined GRE scores can be expected to be over 160? b. What proportion of combined GRE scores can be expected to be under Page 2 of 3 160? c. What proportion of combined GRE scores can be expected to be between 155 and 160? d. What is the probability that a randomly selected student will score over 145 points? e. What is the probability that a randomly selected student will score less than 150 points? f. What is the percentile rank of a student who earns a quantitative GRE score of 142? 5. A Sample of flights is selected, and the times (minutes) required to taxi outare 37, 13, 14, 15, 31, 15. Follow the 4 steps procedure to construct a normal probability plot using Excel. Based on the plot, does the sample appear to be from a population with a normal distribution? 6. Ashley knows that the time it takes her to commute to work is approximately normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes. a) What time must she leave home in the morning so that she is 95% sure of arriving at work by 9 a.m.? b) If Ashley decides to leave at 8: 20 each day for a week (Monday thru Friday), what is the probability that she will be on time for work (i.e. arrive by 9 a.m.) all week? Page 3 of 3