#41, 45-59(odd)

Step 1: Draw a Normal distribution with the horizontal axis labeled scaled using the mean and standard deviation, the area of interest shaded labeled, and unknown boundary value clearly marked. Step 2: Perform calculations-show your work! Do one of the following (i) Use Table A or technology to find the value of z with the indices area under the standard Normal curve, then "unstandardize" transform back to the original distribution; or (ii) Use technology to find the desired area without standardizing. Be sure to answer the question that was asked. To assess Normality for a given set of quantitative data, we first observer shape of a dotplot, stemplot, or histogram. Then we can check how well data fit the empirical rule for Normal distributions. Another good method. assessing Normality is to construct a Normal probability plot. If the Nome probability plot has a linear form, then we can say that the distribution approximately Normal. 2.2 Technology Corners TI-Nspire and other technology instructions are on the book's website at highschool.bfwpub.com/updatedtps6e. 5. Finding areas from values in a Normal distribution Page 121 6. Finding values from areas in a Normal distribution Page 128 7. Making Normal probability plots Page 136 Section 2.2 Exercises 41. Where's the bus? Sally takes the same bus to work web server sends back a response. For one particular pg 111 every morning. The amount of time (in minutes) web server, the time (in seconds) after the start of an that she has to wait for the bus can be modeled by a hour at which a request is received can be modeled uniform distribution on the interval from 0 minutes to by a uniform distribution on the interval from 0 to 10 minutes. 3600 seconds. (a) Draw a density curve to model the amount of time that (a) Sally has to wait for the bus. Be sure to include scales Draw a density curve to model the amount of time after an hour at which a request is received by the web on both axes. server. Be sure to include scales on both axes. (b) On about what percent of days does Sally wait between 2.5 and 5.3 minutes for the bus? (b) About what proportion of requests are received within the first 5 minutes (300 seconds) after the hour? (c) Find the 70th percentile of Sally's wait times. (c) Find the interquartile range of this distribution. 42. Still waiting for the server? How does your web browser get a file from the Internet? Your computer 43. Quick, click! An Internet reaction time test sends a request for the file to a web server, and the asks subjects to click their mouse button as soon as a light flashes on the screen. The light isSection 2.2 Exercises 139 programmed to go on at a randomly selected time 46. Mean and median The figure displays two density after the subject clicks "Start." The density curve curves that model different distributions of quantitative models the amount of time the subject has to wait data. Identify the location of the mean and median by for the light to flash. letter for each graph. Justify your answers. (a) ABC ( b ) AB C Time (sec) until the light flashes 47. Potato chips The weights of 9-ounce bags of a pg 115 particular brand of potato chips can be modeled by a Normal distribution with mean u = 9.12 ounces and (a) What height must the density curve have? Justify your standard deviation o = 0.05 ounce. Sketch the Normal answer. density curve. Label the mean and the points that are (b) About what percent of the time will the light flash more 1, 2, and 3 standard deviations from the mean. than 3.75 seconds after the subject clicks "Start"? 48. Batter up! In baseball, a player's batting average is (c) Calculate and interpret the 38th percentile of this the proportion of times the player gets a hit out of distribution. his total number of times at bat. The distribution of batting averages in a recent season for Major League 44. Class is over! Mr. Shrager does not always let his Baseball players with at least 100 plate appearances statistics class out on time. In fact, he seems to end can be modeled by a Normal distribution with mean class according to his own "internal clock." The M = 0.261 and standard deviation o = 0.034. Sketch density curve models the distribution of the the Normal density curve. Label the mean and the amount of time after class ends (in minutes) when points that are 1, 2, and 3 standard deviations from Mr. Shrager dismisses the class. (A negative value the mean. indicates he ended class early.) 49. Normal curve Estimate the mean and standard deviation of the Normal density curve below. Dismissal time (minutes after class ends) (a) What height must the density curve have? Justify your 5 6 7 8 9 10 11 12 13 14 15 16 17 answer . 50. Normal curve Estimate the mean and standard (b) About what proportion of the time does Mr. Shrager deviation of the Normal density curve below. dismiss class within 1 minute of its scheduled end time? (c) Calculate and interpret the 20th percentile of the distribution. 45. Mean and median The figure displays two density 9112 curves that model different distributions of quantitative 15 data. Identify the location of the mean and median by 20 25 30 letter for each graph. Justify your answers. 51. Potato chips Refer to Exercise 47. Use the empirical pg118 rule to answer the following questions. C (a) About what percent of bags weigh less than 9.02 ounces? Show your method clearly. (a) ABC ( b ) A B (b) A bag that weighs 9.07 ounces is at about what percentile in this distribution? Justify your