To start solving, find the difference between the mean of the data set, and the lower and upper bounds of the given interval.
81.5 %
Practice makes perfect
We know that the set of data is normally distributed with a mean of 100 and a standard deviation of 10. We will find the probability of choosing a value that is between 90 and 120.
90 ≤ x≤ 120
First, let's find the difference between 90 and the mean 100.
90- 100= - 10
Now, let's find the difference between 120 and the mean 100.
120- 100= 20
Then, we will divide the differences by the standard deviation 10.
- 10/10=- 1and20/10=2
Thus, 90 is 1 standard deviation below the mean and 120 is 2 standard deviations above the mean. To find the probability, we will shade the percent of data which is at most 1 standard deviation below the mean and no more than 2 standard deviations above the mean.
Finally, we can find the percent of data by adding the percents of the shaded areas.
