Question 1

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 distribution of scores in a normal distribution is symmetrical around the mean, so the proportion of scores between 0 and -1 standard deviations from the mean is equal to the proportion of scores between 0 and +1 standard deviations from the mean.

Question 2

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

Accepted Answer

This is true. The bell shape refers to the symmetrical curve that is typical of a normal distribution.

Question 3

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

This is a basic property of a normal distribution, where the mean is the midpoint and 50% of the scores fall on either side of the mean.

Question 4

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

Accepted Answer

The definition of standard scores (also known as z-scores) is that they have a mean of 0 and a standard deviation of 1. Therefore, the mean of a set of standard scores will always be 0.

Question 5

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

Accepted Answer

This statement is true. In a normal distribution, approximately 68% of scores fall between -1 and +1 standard deviations, about 95% of scores fall between -2 and +2 standard deviations, and approximately 99.7% of scores fall between -3 and +3 standard deviations.

Question 6

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

Accepted Answer

Standardization changes the mean and standard deviation of the scores but does not affect the shape of the distribution, hence skewness and kurtosis remain unchanged.

Question 7

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, not 20%.

Question 8

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, are calculated by subtracting the mean of a distribution from a raw score and dividing the result by the standard deviation of the distribution. This transformation allows for the direct comparison of scores on different distributions, regardless of their original means and standard deviations.

Question 9

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

Accepted Answer

The answer of In a normal distribution,50% of all scores...

Question 10

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

Accepted Answer

A standard score, also known as a z-score, is a measure of how many standard deviations an observation or data point is above or below the mean of the set of data. By definition, a standard score has a mean of 0 and a standard deviation of 1. Therefore, the standard deviation of a set of standard scores will always be equal to 1.00.

Question 11

All normal distributions reflect empirically real phenomena.

Accepted Answer

While normal distributions are commonly used to model real-world phenomena, not all phenomena necessarily follow a normal distribution.

Question 12

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 any given standard score (z-score) is the same due to the symmetrical nature of the distribution.

Question 13

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 distribution is a measure of its "peakedness" or "flatness". Platykurtic distributions have a flat shape with fewer extreme values than a normal distribution. Standard scores, also known as z-scores, transform the original scores to a standardized scale based on the mean and standard deviation of the distribution. This transformation does not change the shape of the distribution or its kurtosis, only the scale and location. Therefore, a set of scores that is platykurtic will still have the same shape after they have been converted to standard scores.

Question 14

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 15

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 are standardized scores that have a mean of 50 and a standard deviation of 10. So, the statement is true.

Question 16

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 standardizes the scale, so a positively skewed distribution will remain positively skewed.

Question 17

Not all normal distributions are symmetrical about the mean.

Accepted Answer

Normal distributions are defined by their symmetry about the mean, meaning every normal distribution is symmetrically distributed around its mean.

Question 18

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

Accepted Answer

Standardizing scores (e.g., converting to z-scores) does not change the basic shape of the distribution; it only alters the scale, centering the distribution around a mean of 0 and a standard deviation of 1.

Question 19

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

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

Question 20

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

Accepted Answer

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

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