Question

When Kiran runs the 400 meter dash, his finishing times are normally
distributed with a mean of 65 seconds and a standard deviation of 0.5
seconds. Using the empirical rule, what percentage of races will his finishing
time be between 64.5 and 65.5 seconds?

Answer 1

The percentage of races in will his finishing time is between 64.5 and 65.5 seconds is 68%.

What is an empirical rule?

According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% the values lies within one, two, or three standard deviations of the mean of the distribution.

$\rm P(\mu - \sigma \ \ < X < \mu + \sigma) \ \approx 68\%\\\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%$

where we had were mean of the distribution of X is μ and the standard deviation from the mean of the distribution of X is σ (assuming X is normally distributed).

When Kiran runs the 400 meters dash, his finishing times are normally distributed with a mean of 65 seconds and a standard deviation of 0.5 seconds.

Then by the formula, we have

$\rm P (65-0.5 < X < 65+0.5) = P(64.5 < X < 65.5) \approx 68\%$

Learn more about the empirical rule here:

https://brainly.com/question/13676793

#SPJ2