Question

12)On a recent quiz, the class mean was 79 with a standard deviation of 4.3.a) Calculate the z-score for a person who received a score of 95.16)b)  Is 95 an unusual score, according to its Z score?c) How many standard deviations away from the mean is a score of 70?d) Is 70 an unusual score, according to its Z score? POINTSOut OF6e) Explain your answer for d

Answer 1

To calculate a z-score we use the following formula:

$z=\frac{x-\mu}{\sigma}$

where mu represents the mean and sigma represents the standard deviation.

item a)

Given a mean of 79 and a standard deviation of 4.3, the corresponding z-score for a score of 95 is:

$z=\frac{95-79}{4.3}=3.72093023...\approx3.72$

item b)

The range rule of thumb suggests that most values would be in the area covered by four standard deviations, in another words, within two standard deviations above or below the mean.

The z-score absolute value represents how many standard deviations the actual value is from the mean, therefore, 95 is 3.72 standard deviations above the mean, therefore it is an unusual value.

item c)

To find how many standard deviations 70 is from the mean, we calculate its z-score.

$z=\frac{70-79}{4.3}=-2.09302326...\approx-2.09$

he z-score absolute value represents how many standard deviations the actual value is from the mean, therefore, 70 is 2.09 standard deviations below the mean.

item d) and e)

Since 70 is 2.09 standard deviations below the mean, it is an unusual value.