Answer to Question #178947 in Statistics and Probability for Fairuz

Question

The mean time taken by all participants to run a road race was found to be 200 minutes with a

standard deviation of 20 minutes.c. Using the Empirical rule, find the percentage of the runners who ran this road race

completed in-

I. 150 to 250 minutes

II. 110 to 290 minutes

d. Using Empirical rule, find the interval that contains the times taken by at least 99.7% of

all the runners who ran in this road race.

Answer 1

One standard deviation interval (68%):

$(\mu\pm\sigma)=(180,220)$

Two standard deviation interval (95%):

$(\mu\pm2\sigma)=(160,240)$

Three standard deviation interval (99.7%):

$(\mu\pm3\sigma)=(140,260)$

I.

$95\%<P(150<X<250)<99.7\%$

II.

$P(110<X<290)>99.7\%$

d.

$X\leq140$ and $X\geq260$