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Normal distribution

Total questions: 15

Worksheet time: 3hrs 30mins

Name
Class
Date
1.

A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. What percentage ratings can be expected to be between 200 and 275?

a)

43.31%

b)

56.71%

c)

38.61%

d)

29.87%

2.

The lengths of human pregnancies can be described by a Normal model with a mean of 268 days and a standard deviation of 15 days. What percentage of pregnancies will last at least 300 days?

a)

1.64%

b)

98.36%

c)

12.34%

d)

56.19%

3.

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what values should border the middle 50% of the model?

a)

44 and 52 inches

b)

42 and 54 inches

c)

40 and 50 inches

d)

40 and 60 inches

4.

For a recent English exam, the mean was 73 points and the standard deviation was 9.2 points. Find the percent of scores over 85.

a)

9.61%

b)

90.39%

c)

28.51%

d)

75.31%

5.

A standardized test has scores that can be described by a Normal model with a mean score was 100 points and a standard deviation of 10 points. What score is at the 25th percentile?

a)

93.26

b)

106.74

c)

90.32

d)

80

6.

A town has a speed limit of 45 mph. If the speeds of cars traveling in the town can be described by a Normal model with a mean of 48 mph and a standard deviation of 3.5 mph, what percent of cars are exceeding the speed limit?

a)

80.43%

b)

19.56%

c)

23.86%

d)

75%

7.

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what percent of snow fall amounts will be between 40 and 50?

a)

53.93%

b)

46.07%

c)

37.19%

d)

72.34%

8.

A bank's loan officer rates applicants for credit. The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50. What is the rating which cuts off the bottom 20%?

a)

157.92

b)

242.08

c)

189.34

d)

190.60

9.
6.5 CLT:  Red blood cell counts of women are normally distributed with a mean of 4.577 and a standard deviation of 0.382.  What percentage of women have red blood cell counts in the normal range from 4.2 to 5.4?
a)
82.3%
b)
77.8%
c)
72.6%
d)
68%
10.

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 17.5% .

a)

69.98 in

b)

71.18 in

c)

72.40 in

d)

73.01 in

11.
The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviation of 14 inches.  
Suppose a male long jumper's jump ranked in the 75th percentile.  How long was his jump?
a)
0.67 inch
b)
263 inches
c)
272.44 inches
d)
277.25 inches
12.

Suppose the amount of soda in a can is normally distributed; the mean is 16 oz and standard deviation is 0.4 oz. How much soda is in the heaviest 3% of cans?

a)

≈16.97 oz\approx16.97\ oz

b)

≈16.75 oz\approx16.75\ oz

c)

≈16.45 oz\approx16.45\ oz

d)

≈16.30 oz\approx16.30\ oz

13.

Alex's baby was in the 96th percentile for height when she was born. Given σ = 2 inches, and µ = 20 inches, how long was Alex's baby when she was born?

a)

23.5 inches

b)

20.15 inches

c)

17.45 inches

d)

37 inches

14.

Snobby University accepts only those graduate students who score in the top 5% of the GRE (Graduate Requirements Exam).


Given that µ = 151.3 and σ = 8.7, what is the lowest score you can get and still be accepted to SU? Round to the nearest whole number.

a)

165

b)

166

c)

170

d)

162

15.
Professional golfer John Daly is known for his long drives off the tee. Suppose his drives have a mean distance of 315 yards with a standard deviation of 12 yards. What lengths of drives will constitute the middle 60% of all of his drives?
a)
303 yards to 327 yards
b)
0 to 318 yards
c)
312 yards to 318 yards
d)
305 to 325 yards