To start solving, find the difference between the mean score and the given score.
47.5 %
Practice makes perfect
We have been told that the scores on an exam are normally distributed with a mean of 85 and a standard deviation of 5. We will find the percentage of scores that are between 85, which is equal to the mean, and 95.
85 ≤ x≤ 95
First, let's find the difference between 95 and the mean 85.
95- 85= 10
Then, we will divide the difference by the standard deviation 5.
10/5=2
Thus, 95 is 10 standard deviations above the mean and 85, which is equal to the mean, is standard deviations from the mean.To find the percentage, we will shade the percent of data which is at least equal to the mean and at most 10 standard deviations above the mean.
Finally, we can find the percentage of scores by adding the percentages of the shaded areas.
