Question

the scores on a test are normally distributed with a mean of 130 and a standard deviation of 26. what is the score that is 3 standard deviations below the mean? a score of □ is 3 standard deviations below the mean.

Explanation:

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

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

Step2: Identify the values

Given \(\mu = 130\), \(z=- 3\) (since it's below the mean), \(\sigma = 26\).

Step3: Substitute the values into the formula

\(x=130+(-3)\times26\)
\(x = 130-78\)
\(x = 52\)

Answer:

\(52\)