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?

Answer 1

Answer:

B. 55

Step-by-step 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:

$Z = \frac{X - \mu}{\sigma}$

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:

$Z = \frac{X - \mu}{\sigma}$

$1 = \frac{X - 50}{5}$

$X - 50 = 5$

$X = 55$

So the correct answer is:

B. 55