To start solving, find the difference between the mean of the data set and the given interval.
68 %
Practice makes perfect
We know that the set of data is normally distributed with a mean of 50 and a standard deviation of 8. We will find the percent of the data that is between 42 and 58.
42 ≤ x≤ 58
First, let's find the difference between 42 and the mean 50.
42- 50= - 8
Now, let's find the difference between 58 and the mean 50.
58- 50= 8
Then, we will divide the differences by the standard deviation 8.
- 8/8=- 1and8/8=1
Thus, 42 is 1 standard deviation below the mean and 58 is 1 standard deviation above the mean. To find the percent, we will shade the percent of data which is at most 1 standard deviation below the mean and at most 1 standard deviation above the mean.
Finally, we can find the percent of the data by adding the percents of the shaded areas.
