Practice Test 7

Front 1

About what percent of the area under the normal curve is within plus two and minus two standard deviation of the mean?

Back 1

95% (95.5%)

Front 2

What is a graph of a normal probability distribution called?

Back 2

normal curve

Front 3

In a standard normal distribution, ∑ = ______ and σ = ______.

Back 3

zero and one

Front 4

What type of probability distribution is the normal distribution?

Back 4

Continuous

Front 5

In what units does the standardized z value measure distance from the mean?

Back 5

standard deviation

Front 6

What proportion of the area under a normal curve is to the right of a z-score of zero?

Back 6

50% or 0.50

Front 7

What does a z value of –2.00 indicate about the corresponding X value?

Back 7

less than or to the left of the mean, or the X value is 2 standard deviations less than the mean

Front 8

One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it.
What is this property of the normal curve called?

Back 8

asymptotic

Front 9

How is the expected value of a uniform distribution computed ?

Back 9

1/(b-a)

Front 10

One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it. What is this property of the normal curve called?

Back 10

∑ X/ N

Front 11

The shape of any uniform probability distribution is:
A. Negatively skewed
B. Positively skewed
C. Rectangular
D. Bell shaped

Back 11

C. Rectangular

Front 12

The mean of any uniform probability distribution is:
A. (b - a)/2
B. (a + b)/2
C.∑ X/ῃ
D. n^π

Back 12

B. (a + b)/2

Front 13

The standard deviation of any uniform probability distribution is
A. (b – a)/2
B. n ( 1 – π)
C. √[(b-2)^2 / (12)]
D. ∑ P(x)(x-ẍ)^2

Back 13

C.√[(b-2)^2 / (12)]

Front 14

The upper and lower limits of a uniform probability distribution are
A. positive and negative infinity
B. plus and minus three standard deviations.
C. 0 and 1
D. the maximum and minimum values of the random variable.

Back 14

D. the maximum and minimum values of the random variable.

Front 15

What is an important similarity between the uniform and normal probability distributions?
A. The mean, median and mode are all equal.
B. The mean and median are equal
C. They are negatively skewed
D. About 68% of all observations are within one standard deviation of the mean.

Back 15

The mean and median are equal

Front 16

Which of the following is NOT true regarding the normal distribution?
A. Mean, median and mode are all equal
B. It has a single peak
C. It is symmetrical
D. The points of the curve meet the X-axis at z = –3 and z = 3

Back 16

D. The points of the curve meet the X-axis at z = –3 and z = 3

Front 17

For the normal distribution, the mean plus and minus 1.96 standard deviations will include about what
percent of the observations?
A. 50%
B. 99.7%
C. 95%
D. 68%

Back 17

C. 95%

Front 18

Which of the following is NOT a characteristic of the normal probability distribution?
A. Positively-skewed
B. Bell-shaped
C. Symmetrical
D. Asymptotic

Back 18

A. Positively-skewed

Front 19

What is the proportion of the total area under the normal curve within plus and minus two standard
deviations of the mean?
A. 68%
B. 99.7%
C. 34%
D. 95%

Back 19

D. 95%

Front 20

Which of the following is true in a normal distribution?
A. Mean equals the mode and the median
B. Mode equals the median
C. Mean divides the distribution into two equal parts
D. All of the above are correct

Back 20

D. All of the above are correct

Front 21

Tables of normal distribution probabilities are found in many statistics books. These probabilities are
calculated from a normal distribution with
A. a mean of 1 and a standard deviation of 1
B. a mean of 100 and a standard deviation of 15
C. a mean of 0 and a standard deviation of 15
D. a mean of 0 and a standard deviation of 1

Back 21

D. a mean of 0 and a standard deviation of 1

Front 22

Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second
normal distribution has a mean of 10 and a standard deviation of 2. Which of the following it true?
A. the locations of the distributions are different
B. the distributions are from two different families
C. the dispersions of the distributions are different
D. the dispersions of the distributions are the same

Back 22

A. the locations of the distributions are different

Front 23

A random variable from an experiment where outcomes are normally distributed
A. can have any value between -∞ and +∞
B. can have only a few discrete values
C. can have a mean of 0 and a standard deviation of 1
D. can have no values

Back 23

A. can have any value between -∞ and +∞

Front 24

The total area of a normal probability distribution is
A. between –3.0 and 3.0
B. 1.00
C. dependent on a value of 'z'.
D. approximated by the binomial distribution.

Back 24

B. 1.00

Front 25

An area of a normal probability distribution represents
A. a permutation
B. a combination
C. a likelihood
D. a shaded area

Back 25

C. a likelihood

Front 26

The standard normal probability distribution is one which has:
A. A mean of 1 and any standard deviation
B. Any mean and a standard deviation of 1
C. A mean of 0 and any standard deviation
D. A mean of 0 and a standard deviation of 1

Back 26

D. A mean of 0 and a standard deviation of 1

Front 27

What is the distribution with a mean of 0 and a standard deviation of 1 called?
A. Frequency distribution
B. z-score
C. Standard normal distribution
D. Binomial probability distribution

Back 27

C. Standard normal distribution

Front 28

True or False:
The Empirical Rule of probability can be applied to the uniform probability distribution.

Back 28

False

Front 29

True or False:
Areas within a continuous probability distribution represent probabilities.

Back 29

True

Front 30

True or False:
The total area within a continuous probability distribution is equal to 100.

Back 30

False

Front 31

True or False:
The total area within any continuous probability distribution is equal to 1.00

Back 31

True

Front 32

True or False:
For any continuous probability distribution, the probability, P(x), of any value of the random variable, X,
can be computed.

Back 32

False

Front 33

True or False:
The uniform probability distribution's standard deviation is proportional to the distribution's range.

Back 33

True

Front 34

True or False:
For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed.

Back 34

True

Front 35

True or False:
For a uniform probability distribution, the probability of any event is equal to 1/(b-a).

Back 35

False

Front 36

True or False:
For any uniform probability distribution, the mean and standard deviation can be computed by knowing the
maximum and minimum values of the random variable.

Back 36

True

Front 37

True or False:
In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum
values.

Back 37

True

Front 38

True or False:
The uniform probability distribution is symmetric about the mode.

Back 38

False

Front 39

True or False:
Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it.

Back 39

True

Front 40

True or False:
The uniform probability distribution's shape is a rectangle.

Back 40

True

Front 41

True or False:
The uniform probability distribution is symmetric about the mean and median.

Back 41

True

Front 42

True or False:
A continuity correction factor compensates for estimating a discrete distribution with a continuous
distribution.

Back 42

True

Front 43

True or False:
When referring to the normal probability distribution, there is not just one; there is a "family" of
distributions.

Back 43

True

Front 44

True or False:
Some normal probability distributions have equal arithmetic means, but their standard deviations may be
different.

Back 44

True

Front 45

True or False:
The normal curve falls off smoothly in either direction from the central value. Since it is asymptotic, the
curve gets closer and closer to the X-axis, but never actually touches it.

Back 45

True

Front 46

True or False:
The area under the normal curve within plus and minus one standard deviation of the mean is about
68.26%.

Back 46

True

Front 47

True or False:
Some normal probability distributions have different arithmetic means and different standard deviations.

Back 47

True

Front 48

True or False:
For a normal probability distribution, about 95 percent of the area under normal curve is within plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area under the normal curve is within three standard deviations of the mean.

Back 48

True

Front 49

True or False:
Some normal probability distributions are positively skewed.

Back 49

False

Front 50

True or False:
A z-score is the distance between a selected value (X) and the population mean (µ ) divided by the
population standard deviation (σ ).

Back 50

True

Front 51

True or False:
In terms of a formula the standardized value of z is found by z = (X –µ )/σ .

Back 51

True

Front 52

True or False:
The total area under the normal curve is 100%.

Back 52

True

Front 53

True or False:
The normal probability distribution is generally deemed a good approximation for the binomial probability distribution when ῃ π ῃ(1-π) are both greater than five.

Back 53

True

Front 54

True or False:
The number of different normal distributions is unlimited.

Back 54

True

Front 55

True or False:
The mean (µ ) divides the normal curve into two identical halves.

Back 55

True

Front 56

True or False:
The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation
of 1.

Back 56

True

Front 57

True or False:
A z-score is also referred to as the standard normal deviate or just the normal deviate.

Back 57

True

Front 58

True or False:
The mean of a normal distribution is represented by σ.

Back 58

False

Front 59

True or False:
A computed z for X values to the right of the mean is negative.

Back 59

False

Front 60

True or False:
A computed z for X values to the left of the mean is positive.

Back 60

False

Front 61

True or False:
The number of different standard normal distributions is unlimited.

Back 61

False