Question

On a standardized exam for high school seniors in 2013, the mean scale for the mathematics portion of the exam was 514 and the standard deviation was 118. If the scores for this exam are approximately normally distributed, what percent of students taking the exam received a scale score between 396 and 632? Express your answer as a whole percent.

Answer 1

Since the scores are normally distributed, we can use standard normal distribution to answer this question
First we need to convert the scores 396 and 632 in z scores.

Mean scores = 514
Standard deviation = 118

396 converted to z score will be:

`(396-514)/(118) =-1`

632 converted to z score will be:

`(632-514)/(114) =1`

Using the z-table, we are to find the percentage of scores that is between -1 and 1. The value comes to be 0.68 or 68%

So, expressed to nearest whole percent, 68% of students received score between 396 and 632.