Ch. 2 Review 1. The state Employment Service of a certain state certifies the typing speed of applicants. Suppose typing speeds are approximately Normally distributed with a mean of 55 words per minute and a standard deviation of 4 words per minute. If Kim scores at the 95th percentile, then her typing speed is closest to a) b) c) d) e) 47 wpm 50 wpm 59 wpm 62 wpm 63 wpm 2. Golf courses have a wide range of difficulty. Similarly, players differ in ability. In order to adjust for variations between players, they are often assigned a handicap score. To adjust for variations between courses, a handicapper decides to compare the golfer’s score against the data from the course. Suppose course A plays at a mean score of 76 with a standard deviation of 8 strokes with a Normal distribution of scores. The mean score for course B is 80 with a standard deviation of 6 strokes and the scores are Normally distributed. If a golfer regularly shoots an 80 on course A, what should be the comparable score on course B? a) b) c) d) e) 80 83 84 86 88 3. A sales person ranks in the top 5% of all sales people in a large company. If the annual mean sales amount is $750,000 and the standard deviation is $150,000, how much does the person sell each year? a) b) c) d) e) $757,500 $996,750 $1,044,000 $1,697,100 $2,650,500 4. Rainwater was collected in water collectors at 30 different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH units to all of the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are a) b) c) d) e) 5.64, 1.44 5.64, 1.32 5.40, 1.44 5.40, 1.32 5.64, 1.20 5. Studies on the subject of how much high school seniors study per week have indicated that the standard deviation of study time per week is 2.6 hours. Only 10% of the seniors have study times that exceed 20 hours per week. Find the mean number of hours the high school seniors study per week. 6. In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. It was determined that the average speed was 42 mph and the standard deviation was 15 mph. In addition, a histogram revealed that vehicle speed at impact is approximately Normally distributed. Follow the four steps for each problem. a) Between what two numbers did the middle 95% of all the recorded speeds fall? b) What proportion of vehicle speeds were between 30 mph and 55 mph? c) What proportion of vehicle speeds exceeded 70 mph? d) The quintiles (as opposed to quartiles) mark off the points with an area of 0.2, 0.4, 0.6, and 0.8 below them. What are the quintiles of this distribution? (You don’t need to show the four steps for this one) 7. Use the graph below to answer the questions that follow. 4/3 1 2/3 1/3 ½ 1 a) Verify that this is a valid density curve. b) What percent of the observations are within the interval ½ ≤ X ≤ 1? c) What percent of the observations are within the interval X ≤1? d) What percent of the observations are at X = ½? 8. The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150 adults who report drinking alcohol occasionally. About what percent of these adults consume between 4 and 8 ounces per week? Show how you arrived at your answer. Chapter 2 Learning Targets: __ I can explain what “percentile” is and calculate the percentile for a value in a distribution. __ I can construct and interpret ogives (including calculating relative frequency and relative cumulative frequency). __ I can calculate standardized values (z-scores). __ I can describe the effect of a linear transformation on measures of center and spread. __ I can explain why a curve is or is not a “density curve.” __ I can determine the position of the mean and median relative to each other for symmetric and skewed density curves. __ I can describe the shape of a normal distribution. __ I can explain the 68-95-99.7 Rule (a.k.a. the Empirical Rule) and use it to solve problems. __ I can describe the shape, center, and spread of the “standard normal distribution.” __ I can find proportions/percents/percentiles using Table A. __ I can find the value of x in a normal distribution that has a given proportion/percent above or below it. __ I can construct and interpret a normal probability plot to assess normality.