Question

On the ACT Math test, the mean score is 20.5 and the standard deviation is 5.5. The scores are normally distributed. Complete the following:Approximately ___% of the students who took the test in April scored 15 and 26.

Answer 1

Approximately 68.2% of the students who took the test in April scored 15 and 26

Step-by-step explanation:

Since the scores are normally distributed, with a mean of 20.5 and a standard deviation of 5.5, this means that from the mean plus 1 standard deviation there is the 34.1% of the scores. Similarly, the percentage of scores from the mean minus 1 standard deviation is 34.1%

Then:

Mean + 1 standard deviation = 20.5 + 5.5 = 26 ⇒ 34.1%

mean - 1 standard deviation = 20.5 - 5.5 = 15 ⇒ 34.1

This total of this range from 15 to 26 is: 34.1% + 34.1% = 68.2%