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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.