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Normal Distribution Review

Total questions: 21

Worksheet time: 25mins

Name
Class
Date
1.

Which of the following is NOT a characteristic of a Normal Distribution Curve?

a)

It is a continuous bell-shaped curve.

b)

The curve is symmetric about the mean.

c)

The curve is asymptotic about the yy  -axis.

d)

The total area under the curve is 11  .

2.

If XX   is normally-distributed random variable, then the probability that the values of XX  lies within  22  standard deviations of its mean is 95%95\% .

a)

True

b)

False

3.

What can be said about the means and standard deviations of the curves shown in the figure?

a)

The curves have the same means and standard deviations.

b)

The curves have the same means but different standard deviations.

c)

The curves have different means but the same standard deviations.

d)

The curves have different means and standard deviations.

4.
What does σ represent?
a)
sample standard deviation
b)
population/distribution standard deviation
c)
sample mean
d)
population/distribution mean
5.
What does μ represent?
a)
sample standard deviation
b)
population/distribution standard deviation
c)
sample mean
d)
population/distribution mean
6.
What value(s) must you include when defining a normal distribution?
a)
μ
b)
σ
c)
both μ and σ
d)
68, 95 and 99.7
7.
Tests in Mr. Jones class have a mean score of 73 and standard deviation of 6 points. Mark scored a 68 on the test. What is his z-score?
a)
0.83
b)
5
c)
-0.83
d)
-5
8.

What is the total area under the standard normal curve?

a)

0

b)

1/2

c)

1

d)

2

9.

Set up the z score formula for the following information:

A report stated that the average number of times a cat returns to its food bowl during the day is 36. Assume the variable is normally distributed with a standard deviation of 5, and that we wish to find the percentage of cats that return to their dish less than 32 times a day.

a)

z=36325z=\frac{36-32}{5}

b)

z=32365z=\frac{32-36}{5}

c)

z=32536z=\frac{32-5}{36}

d)

z=1365z=1-\frac{36}{5}

10.

What was the median score?

a)

39

b)

50

c)

55

d)

16

11.
This data is normally distributed.  What percent of the data is in the shaded region?
a)
68%
b)

32%

c)
95%
d)
50%
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.

Which measure goes in the center of the Normal Curve?

a)

standard deviation

b)

mean

c)

median

d)

mode

14.
According to the empirical rule, what percentage of data falls within 1 standard deviation? 
a)
25%
b)
68%
c)
95%
d)
99.7%
15.
According to the empirical rule, how much of the data falls within 3 standard deviations? 
a)
25%
b)
68%
c)
95%
d)
99.7%
16.
1.  Which best describes the shaded part of this normal distribution graph?  
a)
All data that is one or higher.
b)
All data that is one or more standard deviations above the mean.
c)
All data that is between 1 and 3.
d)
All data that is above the mean.
17.
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
18.

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.


Find the percentage of golfers that are between 30 and 46 years old.

a)

68%

b)

94%

c)

95%

d)

99.7%

19.
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 between 12 and 15 days?
a)
68%
b)
34%
c)
16%
d)
2.5%
20.
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.
21.

This data is normally distributed. What percent of the data is in the shaded regions?

a)

5%

b)

95%

c)

2.5%

d)

50%