Question

the scores on a test are normally distributed with a mean of 140 and a standard deviation of 28. 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 \(\sigma = 28\). The value of \(\frac{1}{2}\) standard deviation is \(\frac{1}{2}\times\sigma=\frac{1}{2}\times28 = 14\)

Step2: Find the score that is \(\frac{1}{2}\) standard deviation above the mean

The mean \(\mu=140\). The score \(x\) that is \(\frac{1}{2}\) standard deviation above the mean is \(x=\mu+\frac{1}{2}\sigma\)
Substitute \(\mu = 140\) and \(\frac{1}{2}\sigma=14\) into the formula: \(x = 140+14\)

Answer:

\(154\)