Chapter 5

Question 1

The distributions that we have described so far are all empirical distributions—
that is, they are all based on

Answer 1

real data

Question 2

The value of the theoretical normal

distribution lies in the fact that

Answer 2

t many empirical distributions that we study seem to
approximate it. t. We can often learn a lot about the characteristics of these empirical
distributions based on our knowledge of the theoretical normal distribution.

Question 3

Normal distribution

Answer 3

n A bell-shaped and symmetrical theoretical 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.

Question 4

what percent between mean and 1+, 2+ and 3+ resppectively

Answer 4

between the
mean and ±1 standard deviation, 68.26% of all the observations in the distribution occur;
between the mean and ±2 standard deviations, 95.46% of all observations in the
distribution occur; and between the mean and ±3 standard deviations, 99.72% of the
observations occu

Question 5

. When we say that a

variable is “normally distributed,” we mean that the graphic display will

Answer 5

reveal an
approximately bell-shaped and symmetrical distribution closely resembling the idealized
model shown in Figure 5.1. This property makes it possible for us to describe many
empirical distributions based on our knowledge of the normal curve

Question 6

As long as a
distribution is normal and we know the mean and the standard deviation, we can
determine the

Answer 6

proportion or percentage of cases that fall between any score and the mean.

Question 7

This property provides an important interpretation for the standard deviation of empirical
distributions that are approximately normal. For such distributions, when we know the
mean and the standard deviation, we can determine

Answer 7

the percentage or proportion of scores
that are within any distance, measured in standard deviation units, from that distribution’s
mean.

Question 8

The fixed

relationship between the distance from the mean and the areas under the curve applies only

Answer 8

to distributions that are normal or approximately normal.

Question 9

z scores- what are they used to show

Answer 9

We can express the difference between any score in a distribution and the mean in terms of
standard scores,

Question 10

A standard (Z) score is

Answer 10

the number of standard

deviations that a given raw score (or the observed score) is above or below the mean

Question 11

A raw

score can be transformed into a Z score to find

Answer 11

how many standard deviations it is above or

below the mean.

Question 12

To transform a raw score into a Z score, we

Answer 12

divide the difference between the score and the

mean by the standard deviation.

Question 13

A Z score allows us to represent

Answer 13

t a raw score in terms of its relationship to the mean and to
the standard deviation of the distribution

Question 14

The larger the Z score,
236
the larger the difference between

Answer 14

the score and the mean.

Question 15

Standard normal distribution

Answer 15

n A normal distribution represented in standard (Z) scores, with mean = 0 and
standard deviation = 1.

Question 16

Standard normal table

Answer 16

A table showing the area (as a proportion, which can be translated into a percentage)
under the standard normal curve corresponding to any Z score or its fraction.

Question 17

We can also convert proportions or percentages into

Answer 17

z scores

Question 18

To determine the percentile rank of a raw score

requires

Answer 18

s transforming Z scores into proportions or percentages.

Question 19

Converting percentile ranks

to raw scores is based on

Answer 19

transforming proportions or percentages into Z scores. In the
following examples, we illustrate both procedures based on the SAT writing scores data.
(pg 248)

Question 20

The normal distribution is central to …

it also…

Answer 20

The normal distribution is central to the theory of inferential statistics. It also provides a model for
many empirical distributions that approximate normality

Question 21

In all normal or nearly normal curves, we find a

Answer 21

In all normal or nearly normal curves, we find a constant proportion of the area under the curve
lying between the mean and any given distance from the mean when measured in standard
deviation units.

Question 22

The standard normal distribution is …

The proportions corresponding to…

Answer 22

The standard normal distribution is a normal distribution represented in standard scores, or Z
scores, with mean = 0 and standard deviation = 1. Z scores express the number of standard
deviations that a given score is located above or below the mean. The proportions corresponding to
any Z score or its fraction are organized into a special table called the standard normal table