Question

May 18, 11:05:10 PM When Jace runs the 400 meter dash, his finishing times are normally distributed with a mean of 81 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, what percentage of races will his finishing time be between 79.5 and 82.5 seconds?​

Answer 1

68% of races will his finishing time be between 79.5 and 82.5 seconds

Explanation:

Mean time = 81 seconds

Standard deviation = 1.5 seconds

According to the empirical rule : 68%, 95%, 99% lies within 1, 2, and 3 standard deviations of the mean respectively.

Hence, for a finishing time between : 79.5 and 82.5

79.5 = 81 - 1.5 (1 standard deviation to the left of the mean)

82.5 = 81 + 1.5 (1 standard deviation to the right of the mean)

Hence,

79.5 and 82.5 lies within 1 standard deviation from the mean and it is Hence has a percentage of 68%