Question

When Jocelyn runs the 400 meter dash, her finishing times are normally distributed with a mean of 61 seconds and a standard deviation of 2 seconds. Using the empirical rule, what percentage of races will her finishing time be between 57 and 65 seconds?

Answer 1

95% of races will her finishing time be between 57 and 65 seconds.

Explanation:

Mean=61 seconds

Standard deviation =2

Empirical rule says,

68% of data covered between mean±1 standard deviation

95% of data covered between mean ±2 standard deviation

99.7% of data covered between mean ± 3 standard deviation.

I'll upload the Empirical rule curve.

Because 57 is 61-2(2) and 65 is 61+2(2), so, 95% of data covered.

So, according to Empirical rule, 95% of races will her finishing time.