Answer :
The range of distances that includes approximately 95% of the students is 7.8 miles to 24.2 miles.
(a) Approximately 68% of the students have commute distances between 12.9 miles and 19.1 miles.
To find this range, we can use the fact that the mean is 16.0 miles and the standard deviation is 4.1 miles, and use the 68-95-99.7 rule, which states that approximately 68% of the values in a normal distribution fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. Therefore, we can find the range of distances that includes approximately 68% of the students by adding and subtracting one standard deviation from the mean:
16.0 + 4.1 = 20.1
16.0 - 4.1 = 11.9
The range of distances that includes approximately 68% of the students is 11.9 miles to 20.1 miles.
(b) Approximately 95% of the students have commute distances between 7.8 miles and 24.2 miles.
To find this range, we can use the same approach as in (a) and add and subtract two standard deviations from the mean:
16.0 + (2 * 4.1) = 24.2
16.0 - (2 * 4.1) = 7.8
The range of distances that includes approximately 95% of the students is 7.8 miles to 24.2 miles.
To learn more about mean, visit:
brainly.com/question/521501
#SPJ4
