Question 1

A set of scores that is positively skewed will become normally distributed after they have been converted to standard scores.

Accepted Answer

Converting scores to standard scores (z-scores) does not change the shape of the distribution; it only rescales the data. A positively skewed distribution remains skewed even after standardization.

Question 2

In a normal distribution,over 99% of all scores fall between standard scores of -3 and +3.

Accepted Answer

In a normal distribution, approximately 99.7% of all scores fall between standard scores of -3 and +3, which is often referred to as the "68-95-99.7 rule".

Question 3

The process of standardizing scores changes the basic shape of the distribution.

Accepted Answer

Standardizing scores (z-scores) does not change the shape of the distribution; it only rescales the data to have a mean of 0 and a standard deviation of 1.

Question 4

The standard deviation of a set of standard scores is always equal to 1.00.

Accepted Answer

The standard deviation of a set of standard scores is always equal to 1.00 because standard scores (also known as z-scores) are expressed in terms of standard deviations from the mean. By definition, a standard deviation of 1.00 represents one standard deviation unit from the mean, so all z-scores have a standard deviation of 1.00.

Question 5

All normal distributions are characterized by a "bell shape."

Accepted Answer

A bell shape is one of the defining characteristics of a normal distribution. This means that the data is symmetrically distributed around the mean, and the majority of the observations cluster around the mean, with fewer observations at the extremes.

Question 6

The proportion of scores occurring between standard scores of 0 and -1 is less than the proportion of scores occurring between standard scores of 0 and +1.

Accepted Answer

The answer of The proportion of scores occurring between standard...

Question 7

Knowing that a set of scores approximates a normal distribution allows us to make probability statements with respect to those scores,given that we know the mean and standard deviation.

Accepted Answer

A normal distribution is characterized by its mean and standard deviation, and knowing these parameters allows us to calculate probabilities for specific ranges of scores or values. This is due to the well-defined properties of a normal distribution, such as its bell-shaped curve and the fact that a certain percentage of values lie within a certain number of standard deviations from the mean.

Question 8

The mean of a set of standard scores is always equal to 0.

Accepted Answer

The mean of standard scores is calculated by converting the raw scores to z-scores and then taking the average. Since the formula for a z-score subtracts the mean from the raw score, the average of the z-scores will always be 0.

Question 9

Standardization affects the central tendency,variability,skewness,and kurtosis of the scores.

Accepted Answer

Standardization affects the central tendency and variability by centering the data around zero and scaling it, but it does not change the skewness or kurtosis.

Question 10

In some normal distributions,the proportion of scores that occur above or below a given standard score is different.

Accepted Answer

In a normal distribution, the proportion of scores above or below a given standard score (z-score) is always the same due to its symmetrical nature.

Question 11

A set of scores that is platykurtic will still be platykurtic after they have been converted to standard scores.

Accepted Answer

The kurtosis of a set of scores does not change when they are converted into standard scores. The computation of kurtosis involves the deviation of each score from the mean, so converting them to standard scores (which also involves deviations from the mean) does not alter the shape of the distribution.

Question 12

Not all normal distributions are symmetrical about the mean.

Accepted Answer

A normal distribution is defined as being symmetrical about its mean, with the left and right sides of the distribution being mirror images of each other.

Question 13

One important use of standard scores is to compare scores on distributions that have different means and standard deviations.

Accepted Answer

Standard scores (also known as z-scores) allow for the comparison of scores on distributions with different means and standard deviations. By converting scores to z-scores, they can be standardized on a common scale, allowing for meaningful comparisons to be made.

Question 14

It is always the case that 50% of the scores in a normal distribution occur above the mean and 50% of the scores occur below the mean.

Accepted Answer

In a normal distribution, the mean represents the midpoint of the distribution, and the area under the curve is symmetric. Therefore, 50% of the scores fall above the mean and 50% fall below the mean.

Question 15

In a normal distribution,50% of all scores fall between standard scores of -1 and +1.

Accepted Answer

In a normal distribution, approximately 68% of all scores fall between standard scores of -1 and +1.

Question 16

All normal distributions reflect empirically real phenomena.

Accepted Answer

While the normal distribution is a commonly observed pattern in many fields of study, it does not necessarily reflect all empirically real phenomena. There may be instances where data does not follow a normal distribution, or other statistical models may be better suited to describe the phenomenon.

Question 17

T scores are directly analogous to standard scores,but instead of having a mean of 0 and a standard deviation of 1.00,they have a mean of 50.00 and a standard deviation of 10.00.

Accepted Answer

T scores have a mean of 50.00 and a standard deviation of 10.00, not a mean of 0 and a standard deviation of 1.00 like standard scores.

Question 18

In a normal distribution,20% of all scores fall between standard scores of -2 and +2.

Accepted Answer

In a normal distribution, approximately 95% of all scores fall between standard scores of -2 and +2.

Question 19

In most normal distributions,the mean,the median,and the mode are different from each other.

Accepted Answer

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.

Question 20

A standard score in a normal distribution is referred to as a z score.

Accepted Answer

This statement is true. A z score represents the number of standard deviations an observation is above or below the mean in a normal distribution.

Quiz 4: Percentiles,percentile Ranks,standard Scores,and the Normal Distribution