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AP Statistics: Normal Distribution Review
Homework
Name______________________________________
Date____________________________Period______
1. The weights of cockroaches living in a typical college dormitory are approximately distributed with a mean of 80
grams and a standard deviation of 4 grams. The percentage of cockroaches weighing between 77 grams and 83
grams is about:
(a) 99.7%
(b) 95%
(c) 68%
(d) 55%
(e) 34%
2. The average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What is the z-score
of Windex with a cost of 10.1 cents per ounce?
(a) 0.96
(b) 1.31
(c) 1.94
(d) 2.25
(e) 3.00
3. If a density curve was a semicircle, the radius would be approximately:
(a) 0.2
(b) 0.4
(c) 0.6
(d) 0.8
(e) 1
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4. The amount of time a Wilde Lake AP Statistics student spends on homework each evening is approximately normally
distributed. If 22% of the 52 students spend at least 47 minutes doing homework and Erin, who spends 65 minutes
has a standardized score of 1.932, determine:
(a) the mean and standard deviation of the distribution
(b) the approximate number of students who spend less than 15 minutes on homework.
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The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are normally distributed
with µ = 100 and σ = 15.
5. What score would represent the 50th percentile? Explain.
6. Approximately what percent of the scores fall in the range from 70 to 130?
7. A score in what range would represent the top 16% of the scores?
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In a study of elite distance runners, the mean weight was reported to be 63.1 kilograms (kg), with a standard deviation
of 4.8 kg.
8. Assuming that the distribution of weights is normal, sketch the density curve of the weight distribution, with the
horizontal axis marked in kilograms.
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9. Jill scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is
normally distributed with mean 500 and standard deviation 100. Jack takes the ACT mathematics test and scores
27. ACT scores are normally distributed with mean 18 and standard deviation 6. Find the standardized scores for
both runners.
10. Assuming that both tests measure the same kind of ability, who has the higher score, and why?
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Using Table A (table of standard normal probabilities) or your calculator, find the proportion of observations from a
standard normal distribution that satisfies each of the following statements. In each case, sketch the normal curve and
shade the area under the curve that is the answer to the question.
11. Z < –1.5
12. -1.5 < Z < 0
Key:
1)
2)
3)
4)
b)
5)
D
A
D
a) N(35 min, 15.5 min)
about 5 students
A score of 100 will represent the 50th percentile. In a normally distributed set of data, the
mean is also the median, hence the 50th percentile.
6) 95% using the empirical rule or 95.45% using the normalcdf function of the calculator
7) A score of 115 or over will represent the top 16% of the scores.
8) See paper
9) Jill: z = 1.8; Jack: z = 1.5
10) Jill has the higher score because her z-score is higher, which puts her at a higher percentile
ranking for her group, compared to Jack.
11) 6.68%
12) 43.32%
Key:
1)
2)
3)
4)
b)
5)
D
A
D
a) N(35 min, 15.5 min)
about 5 students
A score of 100 will represent the 50th percentile. In a normally distributed set of data, the
mean is also the median, hence the 50th percentile.
6) 95% using the empirical rule or 95.45% using the normalcdf function of the calculator
7) A score of 115 or over will represent the top 16% of the scores.
8) See paper
9) Jill: z = 1.8; Jack: z = 1.5
10) Jill has the higher score because her z-score is higher, which puts her at a higher percentile
ranking for her group, compared to Jack.
11) 6.68%
12) 43.32%