Exercise 23 Page 744

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 80 and 100. 80 ≤ x≤ 100 First, let's find the difference between 80 and the mean 100. 80- 100= - 20Now, let's find the difference between 100 and the mean 100. 100- 100= 0 Then, we will divide the differences by the standard deviation 10. - 20/10=- 2and0/10= Thus, 80 is 2 standard deviations below the mean and 100 is standard deviations from the mean. To find the probability, we will shade the percent of data which is at most 2 standard deviations below the mean and at most equal to the mean.

Finally, we can find the percent of the data by adding the percents of the shaded areas.

The probability of choosing a random value between 80 and 100 is equal to 47.5 %.