Question

The scores on a test are normally distributed with a mean of 110 and a standard deviation of 22. What is the score that is 1 and one half standard deviations below the​ mean?

Answer 1

To calculate the score that is 1.5 standard deviations below the mean of 110 with a standard deviation of 22, multiply 1.5 by 22 to get 33 and then subtract that from the mean. The resulting score is 77.

Step-by-step explanation:

To find the score that is 1 and one half standard deviations below the mean on a normally distributed set of test scores, we use the following formula:

Score = mean + (Z-score × standard deviation)

Given that the mean is 110 and the standard deviation is 22, we can calculate:

Score = 110 + (-1.5 × 22)

First, calculate 1.5 times the standard deviation:

1.5 × 22 = 33

Now, since the Z-score is -1.5 (meaning 1.5 standard deviations below the mean), we multiply this by -1:

33 × -1 = -33

So, subtract 33 from the mean:

110 - 33 = 77

The score that is 1.5 standard deviations below the mean is 77.