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AP Statistics: Normal Distributions Practice WS Name __________________________________________ #_____ (1) Below is data about the survival times (in days) of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment. 43 80 91 103 137 191 45 80 92 104 138 198 53 81 92 107 139 211 56 81 97 108 144 214 56 81 99 109 145 243 57 82 99 113 147 249 58 83 100 114 156 329 66 83 100 118 162 380 67 84 101 121 174 403 73 88 102 123 178 511 74 89 102 126 179 522 79 91 102 128 184 598 (a) Enter the data into L1 on your calculator. Construct a normal probability plot of the data. What conclusion would you draw about the approximate normality of the data? (b) Use your calculator to make a histogram of the data. How does the shape of the histogram support your conclusion in part (a)? For questions 2 through 4, draw, label, and shade a curve, show steps of calculation, and write a conclusion sentence. (2) Consider the variable X = time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of X is well approximated by a normal curve with mean 45 min and standard deviation 5 min. (a) If 50 min is allowed for the exam, what proportion of students at this university would be unable to finish in the allotted time? (b) How much time should be allowed for the exam if we wanted 90% of the students taking the test to be able to finish in the allotted time? (c) How much time is required for the fastest 25% of all students to complete the exam? (3) Data from the article “The Osteological Paradox: Problems in Inferring Prehistoric Health from Skeletal Samples” suggests that a reasonable model for the distribution of the continuous numerical variable x = height of a randomly selected 5-year-old child is a normal distribution with a mean of µ = 100 cm and standard deviation σ = 6 cm. What proportion of the heights is between 90 and 110 cm? (4) When Tiger Woods is on the driving range, the distance that golf balls travel when he hits them with a driver follows a Normal distribution with a mean of 310 yards and a standard deviation of 8 yards. Find the 33rd percentile of Tiger’s drive distance distribution. Use the empirical rule (and only the empirical rule) to answer the following questions. (5) Grades on a recent AP Psychology test are (b) Between what values do 95% of all test grades normally distributed with a distribution N(88, 2.4). falls? ________________________ (a) Sketch a normal curve to represent this distribution. (c) How well did the top 2.5% of all test takers do? ________________________ (d) If someone’s grade was reported at the 16th percentile, about what grade would the student have earned? __________ 84th percentile? ________ (e) A test grade of 83.2 would be at the __________ percentile.