Z-Scores

Using a z-table, what is the area beyond a z of 3.43?

.0003

A social researcher has constructed a measure of racial prejudice and obtained a distribution of scores on this measure from a randomly selected sample of public office holders. The scores were normally distributed with a mean of 45 and a standard deviation of 7. What is the approximate probability that a randomly selected case from the sample will have a score less than 38?

.1587

The probability that a randomly selected case will have a score beyond ±1.00 standard deviation of the mean is:

.3174

Using a z-table, what is the area between the mean and a z of 1.71?

.4564

Using a z-table, what is the proportion are above the mean?

.5000

A standard normal curve will have a mean of _____ and a standard deviation of _____.

0, 1

If for three individuals the obtained z-scores were 3.00; -2.00; and 1.64, what percentage of individuals scored higher than them, respectively, according to the z-table?

0.13%, 97.72%, and 5.00%

Using a z-table, if the area between the mean and z is .1179, what is the corresponding z?

0.30

The mean of a set of scores is 5.0, the variance is 4.00, the standard deviation is 2.0, and the mode is 3.5. What is a score of 8.00 expressed as a z-score?

1.50

If a distribution has a mean of 100 and a standard deviation of 15, what value would be +2 standard deviations from the mean?

130

If a normal distribution of scores has a mean of 100 and a standard deviation of 10, what percentage of scores would lie above 2 standard deviations?

2.28%

If a distribution has a mean of 35 and a standard deviation of 5, what value would be -2.5 standard deviations from the mean?

22.5

Some z-score tables give the area between a score and the mean. For a z-score of -1.00 that area (in percentages) is:

34.13%

What percentage of scores lies between the mean and -1 standard deviation for a normal distribution with a mean of 100 and a standard deviation of 15?

34.13%

If a distribution has a mean of 35 and a standard deviation of 5, what value would be +1.5 standard deviations from the mean?

42.5

The area beyond ±2 standard deviations contains approximately what percentage of the area under the normal curve?

5%

Given a population distribution of women's heights with a mean of 5 feet 6 inches, which value is least probable?

6 feet 1 inch

The area between the mean and a z-score of +1.50 is 43.32%. This score is less than _____ of the scores in the distribution.

6.68%

For all normal curves the area between the mean and ±1 standard deviation will be:

68.26% of the total area

A student's score on her midterm exam was at the 50th percentile and the grades were normally distributed. The exam average was 78 and the standard deviation was 6. What was her score on the exam?

78

Approximately what percentile rank is associated with a z-score of +1.00?

84

What two scores would divide a normal distribution such that 68.26% of the general population falls within them if the mean is 100 and the standard deviation is 15?

85 to 115

The area between the mean and a z-score of +1.50 is 43.32%. This score is higher than _____ of the scores in the distribution.

93.32%

Approximately how many people would have scores LOWER than an individual with a z-score of 1.96?

97.5%

A z-score of 2.3 on a normally distributed measure corresponds to a percentile rank of:

98.93

What percentage of scores will fall between -3 and +3 standard deviations in a normal distribution?

99.74%

Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and a score of 90 on a test with a mean of 80 and a standard deviation of 8.

A score of 90 with a mean of 80 and a standard deviation of 8 is better.

Which of the following is not true about the z-score distribution?

The z-distribution always looks normal.

In the z-score formula, the mean is subtracted from:

a given score

The standardized normal distribution or z-distribution has:

a mean of 0 and a standard deviation of 1

Assuming a normal distribution of 1,000 cases, how many cases will be farther away from the mean than +3 standard deviations?

about 1

The area between a negative z-score and a positive z-score can be found by:

adding the areas between each z-score and the mean

The z-scores of two tests scores are +1.2 and +1.5. To obtain the area between these scores:

find the area between each score and the mean in the z-score table and then subtract the smaller area from the larger area

The area between two negative z-scores can be found by:

finding the area between each z-score and the mean and subtracting the smaller area from the larger

The z-distribution:

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

Converting a score to a z-score allows a researcher to:

locate where a score falls in a distribution and describe how it compares to other scores in the distribution.

The normal curve represents a distribution where the __________, ___________, and ___________ are equal to each other.

mean / median / mode

The tails of the theoretical normal curve:

never touch the horizontal axis

A proportion or area under the curve can also represent the:

probability of a score occurring

As used in the social sciences, probabilities are a type of _____ which can vary from _____.

proportion, 0.00 to 1.00

Converting scores into z- scores standardizes the original distribution to units of the:

standard deviation

z-scores are:

standardized scores

By definition, the normal curve is

symmetrical

A z-score of -3.0 means:

that the score is below the sample mean.

Statistical measures like z-scores are used to establish:

the relative position of a single score to all other scores.

If a z-score is 0 then the value of the corresponding raw score would be:

the same as the mean of the empirical distribution

In the z-score formula, the denominator is:

the standard deviation

A defining characteristic of normal curve is that they are:

theoretical

If a distribution has a mean of 50 and a standard deviation of 5, what value would be -1 standard deviation from the mean?

45

Which of the following statements is true concerning normal distributions?

The distribution is symmetrical

As the standard deviation of a normal distribution increases, the proportion of the area between ±1 standard deviation will:

stay the same