Question

A student is given data that follows a normal distribution. According to the data, the mean amount of time that students spent reading outside of school each month was 10 hours, and the standard deviation was 2 hours. The student creates a normal distribution curve to model the situation and labels the curve so that 34% of the students fall in the range between 10 and 12 hours. Select the information that justifies the student's labeling.

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.
b. Only 95% of the students will fall in the range of 10-2 and 10+2 hours
c. Only 68% of the students will fall in the range of 10-6 and 10+6 hours
d. Only 95%of the students will fall in the range of 10 -8 and 10 + 8 hours.

Answer 1

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.

Explanation:

He appies the empirical 68-95-99.7 rule, where 68% of the data is expected to be within ne standard deviation from the mean, to the right and to the left.

Half of this (68%/2=34%) will be between the mean and one deviation standard to the right. This is between 10 hours and 10+2=12 hours.

The right answer is:

a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.