Question

the scores on a test are normally distributed with a mean of 40 and a standard deviation of 8. 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 into the formula

Given \(\mu = 40\), \(z = 1\) (since it's 1 standard deviation above the mean), and \(\sigma=8\).

$$x = 40+1\times8$$

Step3: Calculate the value of \(x\)

$$x=40 + 8=48$$

Answer:

48