Question

A race director is preparing for an upcoming marathon and estimates that the mean time to

Answer 1

93.06% of the race is longer than 236 minutes.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation$

Given that μ = 310, σ = 50

For x > 236:

$z=\frac{236-310}{50}=-1.48$

From the normal distribution table:

P(x > 236) = P(z > -1.48) = 1 - P(z < -1.48) = 1 - 0.0694 = 0.9306 =  93.06%

93.06% of the race is longer than 236 minutes.

Find out more on z score at: brainly.com/question/25638875