Deck 5: The Normal Distribution

Question 1

What percentage of the area under the normal curve falls between ±3 standard deviations?

A)99.72
B)95.46
C)68.26
D)20.00

Answer 1

99.72

Question 2

Suppose that in a particular sample,the mean is 70.07 and the standard deviation is 10.27.What is the Z score that corresponds to a raw score of 80?

A)0.97
B)6.82
C)9.93
D)14.61

Answer 2

0.97

Question 3

A normal distribution represented in Z scores is referred to as a:

A)normal distribution.
B)normal bell-curve.
C)standard normal distribution.
D)standard normal table.

Answer 3

standard normal distribution.

Question 4

A normal distribution represented in standard Z scores,with

A)mean = 0 and standard deviation = 1.
B)mean = 1 and standard deviation = 0.
C)mean = 0 and standard deviation = 0.
D)mean = 1 and standard deviation = 1.

Question 5

The number of standard deviations that a given raw score is above or below the mean is referred to as a

A)mean.
B)frequency distribution.
C)variance.
D)standard (Z)score.

Question 6

For a Z score of zero,what is the proportion of area between the mean and the Z score?

A)0.0
B).05
C).50
D)1.0

Question 7

The normal distribution is central to the theory of ______ statistics.

A)inferential
B)descriptive
C)standardized
D)biserial

Question 8

Considering the properties of the normal curve,if we know the mean and standard deviation,we are then able to calculate the ______ under the curve between any score and the mean.

A)range
B)area
C)mean
D)mode

Question 9

The normal distribution is a ______ and ______ symmetrical distribution with the mean,the median,and the mode all coinciding at its peak and with the frequencies gradually decreasing at both ends of the curve.

A)bell-shaped;empirical
B)bell-shaped;theoretical
C)curvilinear;hypothetical
D)curvilinear;inferential

Question 10

For a Z score of zero,what is the proportion of area beyond the Z score?

A)0.0
B).05
C).50
D)1.0

Question 11

To find the percentile rank of a given score,it is necessary to determine the area

A)between the mean and the Z score.
B)below the Z score.
C)above the Z score.
D)equal to the mean.

Question 12

A standard normal table shows the area under the standard normal curve corresponding to any ______ or its fraction.

A)bell-curve
B)Z score
C)raw score
D)standard deviation

Question 13

What percentage of the area under the normal curve falls between ±1 standard deviations?

A)99.72
B)95.46
C)68.26
D)20.00

Question 14

What percentage of the area under the normal curve falls between ±2 standard deviations?

A)99.72
B)95.46
C)68.26
D)20.0

Question 15

Suppose that in a particular sample,the mean is 70.07 and the standard deviation is 10.27.What is the Z score for a raw score of 65?

A)-0.49
B)0.49
C)-0.51
D)0.51

Question 16

Suppose that the area above some Z score is 0.31,which when multiplied by 100 equals 31%.What is the term for this quantity?

A)The mean
B)The standard deviation
C)The proportion between the mean and the Z score
D)The percentile rank

Question 17

Suppose that in a particular sample,the mean is 70.07 and the standard deviation is 10.27.What is the raw score associated with a Z score of 1.88?

A)80.54
B)88.00
C)89.38
D)90.27

Question 18

Suppose that in a particular sample,the mean is 50 and the standard deviation is 10.What is the Z score associated with a raw score of 68?

A)1.8
B)2
C)-1.8
D)11.8

Question 19

To find proportion of the area under the normal curve between two Z scores,one below the mean and the other above the mean,it is necessary to examine the

A)sum of the areas between each Z score and the mean.
B)difference of the areas between each Z score and the mean.
C)sum of the areas beyond each Z score and the mean.
D)difference of the areas beyond each Z score and the mean.

Question 20

To find proportion of the area under the normal curve between two Z scores that are both above the mean,it is necessary to examine the

A)quotient obtained by dividing the larger Z score by the smaller.
B)product obtained by multiplying the smaller Z score by the larger Z score.
C)difference between the areas beyond each Z score.
D)sum of the areas associated with each Z score.

Question 21

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.For a first age at marriage of 33.44,the proportion of area beyond the Z score associated with this age is 0.05 .What is the percentile rank for this score?

Question 22

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.The Z score associated with the top 5% of the distribution is approximately 1.65.What is the observed age at first marriage associated with this Z score?

Question 23

Probability can be calculated as: Number of times an event will occur/Total number of events.

Question 24

Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52.Then the cut-off point for the top 30% is 270.

Question 25

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.Suppose that the proportion of area between the mean and two Z scores of ±0.35 is 0.14.Calculate the raw scores associated with these two Z scores.What proportion of respondents were first married between these two ages?

Question 26

The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18.Calculate the Z score associated with three siblings.

Question 27

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.Calculate the Z score associated with an observed age at first marriage of 25.50 and provide a substantive interpretation of this quantity.

Question 28

The normal distribution is a theoretical distribution.

Question 29

SELECT ALL THAT APPLY.The normal distribution is

A)right skew symmetric.
B)left skew symmetric.
C)symmetric.
D)bell-shaped.

Question 30

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.Suppose that a person experienced their first marriage at age 23.If the area beyond the Z-score associated with age 23 is 0.24,what proportion of respondents experienced their first marriage after age 23?

Question 31

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.Calculate the observed age at first marriage associated with a Z score of -0.72.

Question 32

SELECT ALL THAT APPLY.Which of the following coincide in a normal distribution?

A)mean
B)median
C)variance
D)mode

Question 33

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.Suppose that a person experienced their first marriage at age 23.If the area beyond the Z score associated with age 23 is 0.24,what proportion of respondents experienced their first marriage before age 23?

Question 34

Rare events,with smaller corresponding probabilities,are towards the middle of the normal curve.

Question 35

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.Calculate the Z score associated with an observed age at first marriage of 25.50.

Question 36

The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18.Calculate the Z score associated with three siblings and provide a substantive interpretation of this quantity.

Question 37

The mean age at first marriage for respondents in a survey is 23.33,with a standard deviation of 6.13.The Z score associated with a particular age at first marriage is 0.35.If the proportion of the area between this particular age at first marriage and the mean is 0.14,what proportion of respondents experienced their first marriage earlier than this age?

Question 38

SELECT ALL THAT APPLY.The area under the normal curve is

A)68.28% between the mean and ±2 standard deviation.
B)equal to 1.00 or 100% of the total observations.
C)divided into two equal parts by a vertical line through the mean.
D)a proportion or percentage of the number of observations.

Question 39

Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52.Then the score which corresponds to the bottom 24% is 199 or lower.

Question 40

In a normal distribution,there is a constant proportion of the area under the curve lying between the mean and any given distance from the mean and is measured in

A)variance units.
B)Z score units.
C)raw score units.
D)standard deviation units.

Question 41

Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52.How high must an individual score to be in the highest 10%?

Question 42

Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52.Identify the scores which correspond to the bottom 5%?

Question 43

The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18.The standard normal table reports the following information in the table below.Calculate the proportion of respondents who had more than two siblings.

Question 44

The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18.Calculate the Z score associated with two siblings.

Question 45

Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52.What is the percentile rank of a raw score 287?

Question 46

The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18.The standard normal table reports the following information in the table below.Calculate the percentile rank for three siblings.

Question 47

The mean number of siblings for respondents in a survey is 3.76 with a standard deviation of 3.18.The standard normal table reports the following information in the table below.Calculate the proportion of respondents who had between two and three siblings.

Question 48

Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52.What is the percentile rank of a raw score 155?

Question 49

The annual salaries of employees in a large company are normally distributed with a mean of $50,000 and a standard deviation of $20,000.What percent of people earn between $45,000 and $65,000?

Question 50

In a normal distribution with a mean of 3.76 and a standard deviation of 3.18,how many standard deviations from the mean is the 95th percentile?