Question

the scores on a test are normally distributed with a mean of 50 and a standard deviation of 10. what is the score that is 3 standard deviations below the mean? a score of \\(\square\\) is 3 standard deviations below the mean.

Explanation:

Step1: Recall the formula for deviation from mean

To find a score \( x \) that is \( k \) standard deviations below the mean \( \mu \), we use the formula \( x=\mu - k\times\sigma \), where \( \sigma \) is the standard deviation. Here, \( \mu = 50 \), \( k = 3 \), and \( \sigma=10 \).

Step2: Substitute the values into the formula

Substitute \( \mu = 50 \), \( k = 3 \), and \( \sigma = 10 \) into the formula: \( x=50-3\times10 \).
First, calculate \( 3\times10 = 30 \). Then, \( 50 - 30=20 \).

Answer:

20