Question

the scores on a test are normally distributed with a mean of 100 and a standard deviation of 20. what is the score that is \\( \frac { 1 } { 2 } \\) standard deviation above the mean? a score of \\( \square \\) is \\( \frac { 1 } { 2 } \\) standard deviation above the mean

Explanation:

Step1: Calculate the value of \(\frac{1}{2}\) standard deviation

The standard deviation \(\sigma = 20\).
\(\frac{1}{2}\sigma=\frac{1}{2}\times20 = 10\)

Step2: Find the score above the mean

The mean \(\mu=100\).
The score \(x=\mu+\frac{1}{2}\sigma\)
Substitute \(\mu = 100\) and \(\frac{1}{2}\sigma=10\) into the formula:
\(x = 100+10=110\)

Answer:

\(110\)