Question

the scores on a test are normally distributed with a mean of 150 and a standard deviation of 30. what is the score that is $\frac{1}{2}$ standard deviation above the mean? a score of 165 is $\frac{1}{2}$ standard deviation above the mean.

Explanation:

Step1: Identify the formula

The formula to find a value \(x\) that is \(z\) standard - deviations above the mean \(\mu\) is \(x=\mu + z\sigma\), where \(\mu\) is the mean, \(z\) is the number of standard - deviations, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values

We are given that \(\mu = 150\), \(z=\frac{1}{2}\), and \(\sigma = 30\). Substitute these values into the formula: \(x=150+\frac{1}{2}\times30\).

Step3: Calculate the result

First, calculate \(\frac{1}{2}\times30 = 15\). Then, \(x=150 + 15=165\).

Answer:

165