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 1 standard deviation above the mean? a score of is 1 standard deviation above the mean.

Explanation:

Step1: Recall the formula for a value \(x\) in a normal distribution

The formula is \(x=\mu + z\sigma\), where \(\mu\) is the mean, \(z\) is the number of standard deviations from the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values

Given \(\mu = 150\), \(z = 1\) (since we want 1 standard deviation above the mean), and \(\sigma=30\).
Substitute into the formula: \(x = 150+1\times30\).

Step3: Calculate the value of \(x\)

\(x=150 + 30=180\).

Answer:

180