Question

In a set of scores with a mean of 50 and a standard deviation of 5, what raw score is represented be a z-score of 1.00?

A. 30
B. 55
C. 60
D. 20

Answer 1

B. 55

Explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 50, \sigma = 5`

What raw score is represented be a z-score of 1.00?

This is X when Z = 1. So:

`Z = (X - \mu)/(\sigma)`

`1 = (X - 50)/(5)`

`X - 50 = 5`

`X = 55`

So the correct answer is:

B. 55