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Normal Distribution Question Bank

Total questions: 53

Worksheet time: 2hrs 22mins

Name
Class
Date
1.

Where can we locate the mean in the normal curve?

a)

to the left portion

b)

to the right portion

c)

at the center

d)

on the z - axis

2.

What is the total area under the normal curve in a standard normal distribution?

a)

1

b)

2

c)

3

d)

4

3.
A z-score tells you...
a)
the standard deviation of a sampling distribution.
b)
the original raw score on which it is based.
c)
if the distribution it comes from is normal.
d)
how many standard deviations away from the mean a score lies.
4.
Find the area under the standard normal curve to the right of z = -2.67.
a)
0.0869
b)
0.9962
c)
0.0008
d)
0.1234
5.
Find the area under the normal distribution curve to the left of 
Z=0.27.
a)
0.3936
b)
0.3897
c)
0.6064
d)
0.4892
6.
Find the area under the normal distribution curve between 
z=-1.53 and z=0.
a)
0.437
b)
0.563
c)
0.500
d)
0.063
7.
Find the area under the standard normal curve to the right of z = -2.67.
a)
0.0869
b)
0.9962
c)
0.0008
d)
0.1234
8.
Find the area under the normal distribution curve between a z=-1.26 and z=.57. 
a)
0.0047
b)
0.9204
c)
0.6119
d)
0.4981
9.
Adam's Z-score on a test is +2.5.  What does this mean?
a)
He'd better start studying.
b)
He did better than EVERYONE.
c)
He scored 2.5 standard deviations above the average.
d)
He did terrible.
10.
If Gonzalo's score is 87, the class average is 82, and the SD is 4, what is Gonzalo's Z-score?
a)
-1.25
b)
+1.25
c)
+1.20
d)
+1.02
11.
The normal curve is symmetrical about the mean.
a)
True
b)
False
12.
This data is normally distributed.  What percent of the data is in the shaded region?
a)
68%
b)
95%
c)
99.7%
d)
50%
13.
A z-score tells you...
a)
the standard deviation of a sampling distribution.
b)
the original raw score on which it is based.
c)
if the distribution it comes from is normal.
d)
how many standard deviations away from the mean a score lies.
14.
Find the area of the shaded region if the z-score is 1.25
a)
0.1056
b)
0.8944
c)
0.8849
d)
0.1151
15.
Find the area of the shaded region if the z-score is 0.75
a)
0.2266
b)
0.7734
c)
0.758
d)
0.242
16.
What shape is a normal distribution curve?
a)
Half curve
b)
Round curve
c)
Bell curve
d)
Square curve
17.
Between what two standard deviations of a normal distribution contain 68% of the data?
a)
one below and one above
b)
two below and two above
c)
two below and zero
d)
zero and two above
18.
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last 6 days or less?
a)
68%
b)
34%
c)
16%
d)
2.5%
19.
What shape is a normal distribution curve?
a)
Half curve
b)
Round curve
c)
Bell curve
d)
Square curve
20.
Between what two standard deviations of a normal distribution contain 68% of the data?
a)
one below and one above
b)
two below and two above
c)
two below and zero
d)
zero and two above
21.
The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. What percent of men are between 64 and 66.5 inches tall? 
a)
50%
b)
2.5%
c)
13.5%
d)
34%
22.
The distribution of heights of adult American men is approximately Normal with mean 69 inches and standard deviation 2.5 inches. Between what heights do the middle 95% of men fall? 
a)
66.5-71.5
b)
64-74
c)
61.5-76.5
d)
65-73
23.

Given a mean of 75 and a standard deviation of 7, what percentage of scores are between 75 and 82?

a)

68%

b)

81.5%

c)

16%

d)

34%

24.

The average weight of a newborn is 7.5 pounds, with a standard deviation of 1.25 pounds. Birth weight follows the standard normal curve. What percent of newborns weigh 5 pounds or less at birth?

a)

2.35%

b)

0.15%

c)

2.5%

d)

50%

25.

What is the formula to find the corresponding z-score for population data?

a)

z = X - μ / σ

b)

z = (X - μ) / σ

c)

z = μ - X / σ

d)

z = (μ - X) / σ

26.

Which of the following is NOT TRUE?

a)

The mean, median, and the mode are equal.

b)

The curve is asymptotic to the base line.

c)

The total area under the curve is less than 1.

d)

The curve is symmetrical about its center.

27.

Find the z-score for 48 given a mean of 50 and a standard deviation of 5.

a)

2.5

b)

-2.5

c)

-0.4

d)

0.4

28.

Students pass a test if they score 50% or more.


The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.


Assuming this data is normally distributed, what percentage of students pass the test? in percentage...

a)

5

b)

16

c)

24

d)

32

29.

A test has a mean of 40 and a standard deviation of 10. What is the percent of people that scored between 30 and 40?

a)

68%

b)

34%

c)

13.6%

d)

100%

30.

Find the z-score for 75 given a mean of 60 and a standard deviation of 6.

a)

-2.5

b)

2.5

c)

-1.15

d)

1.15

31.
What is the shape of the distribution?
a)
Skewed Left 
b)
Skewed Right
c)
Symmetric
d)
Bimodal
32.

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%

33.

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%

34.

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

35.

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%

36.

Determine Pr(23 < X < 27) given µ = 24, σ = 3

a)

4.37%

b)

63.06%

c)

47.19

d)

47.19%

37.

The average height of NBA basketball players is 79 inches with a standard deviation of 1.75 inches. Approximately what percent of the players are taller than 82 inches?

a)

about 4% to 5%

b)

about 2% to 3%

c)

about 6% to 7%

d)

about 6.5%c to 7.5%

38.

The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with mean of 1497

and standard deviation of 322. Calculate the z-score of a student earning a score of 1980.


.

a)

2

b)

1.5

c)

1.75

d)

2.25

39.
According to the empirical rule, what percentage of data falls within 1 standard deviation? 
a)
25%
b)
68%
c)
95%
d)
99.7%
40.
The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?
a)
0.6915
b)
0.1762
c)
0.8238
d)
-0.93
41.

Use the following information and the Empirical Rule to estimate the answer.


The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.


There are 500 golf members at the Mathy Country Club. How many are younger than 34?

a)

16

b)

80

c)

100

d)

150

42.
What is the Normal Range (68%) of the annual precipitation for Phoenix, if the average is 29 with a standard deviation of 3?
a)
26-32
b)
3-29
c)
26-29
d)
39-32
43.
The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.
a)
 28,000 km and 32,000 km.
b)
24,000 km and 34,000 km.
c)
26,000 km and 34,000 km.
d)
27,000 km and 31,000 km.
44.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?
a)
68%
b)
99.7%
c)
95%
d)
84%
45.

In a Memorial Day 5K race the mean time that it takes the runners to complete the course is 48 minutes with a standard deviation of 6 minutes. Find the probability that a runner finished between 36 and 54 minutes.

a)

81.86%

b)

88.6 %

c)

11.4%

d)

84.62%

46.

In a Memorial Day 5K race the mean time that it takes the 54 runners to complete the course is 48 minutes with a standard deviation of 6 minutes. Find the approximate number of the 54 runners that finish less than 36 minutes.

a)

7

b)

1

c)

2

d)

5

47.

In a Memorial Day 5K race the mean time that it takes the 54 runners to complete the course is 48 minutes with a standard deviation of 6 minutes. Find approximate number of runners to finish in more than 54 minutes

a)

9

b)

7

c)

5

d)

3

48.

The times needed to check out at a local grocery store are normally distributed with a mean of 110 seconds and a standard deviation of 20 seconds.

About what percent of shoppers check out between 90 seconds and 130 seconds.

a)

68%

b)

95%

c)

97.5%

d)

65%

49.

The times needed to check out at a local grocery store are normally distributed with a mean of 110 seconds and a standard deviation of 20 seconds.

About what percent of shoppers check out over 2 minutes?

a)

31%

b)

41%

c)

21%

d)

50%

50.

In a large group of earthworms collected for study, the lengths of earthworms are normally distributed with a mean of 8.4 centimeters and a standard deviation of 1.6 centimeters. What percent of earthworms are expected to be longer than 10 centimeters

a)

16%

b)

5%

c)

2.35%

d)

64%

51.

In a large group of earthworms collected for study, the lengths of earthworms are normally distributed with a mean of 8.4 centimeters and a standard deviation of 1.6 centimeters. What percent of earthworms are at most 8 centimeters?

a)

40.1%

b)

50%

c)

2.3.5%

d)

64%

52.

In a large group of earthworms collected for study, the lengths of earthworms are normally distributed with a mean of 8.4 centimeters and a standard deviation of 1.6 centimeters. What percent of earthworms are between 6 and 9 centimeters?

a)

40.1%

b)

50.94%

c)

57.94%

d)

64%

53.

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%