Question

When Gabriella runs the 400 meter dash, her finishing times are normally distributed with a mean of 79 seconds and a standard deviation of 0.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 95% of her finishing times in the 400 meter race.

Answer 1

(78, 80)

Explanation:

Given a normal distribution :

Mean = 79 seconds

Standard deviation = 0.5 seconds

Using the empirical rule :

95% of her finishing times :

According to the empirical rule, 95% represents 2 standard deviations from the mean that is ± 2 standard deviations from the mean score or value.

Hence ;

The interval will be defined as ;

Mean ± 2(standard deviation)

79 ± 2(0.5)

79 ± 1

(79 - 1) ; (79 + 1)

78 ; 80