Question

the scores on a test are normally distributed with a mean of 90 and a standard deviation of 18. what is the score that is 2 standard deviations above the mean? a score of \square is 2 standard deviations above the mean.

Explanation:

Step1: Recall the formula for a score \( x \) that is \( z \) standard deviations above the mean \( \mu \). The formula is \( x=\mu + z\times\sigma \), where \( \mu \) is the mean, \( z \) is the number of standard deviations, and \( \sigma \) is the standard deviation.

Here, \( \mu = 90 \), \( z = 2 \), and \( \sigma = 18 \).

Step2: Substitute the values into the formula.

\( x=90 + 2\times18 \)
First, calculate \( 2\times18 = 36 \). Then, \( 90+36 = 126 \).

Answer:

126