To start, find the difference between the given score and the mean score.
47.5 %
Practice makes perfect
We have been told that the scores on a test are normally distributed with a mean of 74 and a standard deviation of 8. We will find the percentage of juniors whose score is between 58 and 74, which is the mean.
58 ≤ x≤ 74
First, let's find the difference between the mean and 58.
74-58= 16
Then, we will divide the difference by the standard deviation 8.
16/8=2
Thus, 58 is 2 standard deviations below the mean.
To find the total percentage of juniors whose score is between 58 and 74, we will shade the percent of data which is no more than 2 standard deviations below the mean.
Finally, we can find the percentage of juniors by adding the percentages of the shaded areas.
