Question

The length of time needed to complete a certain test is normally distributed with mean 46 minutes and standard deviation 6 minutes. Find the probability that it will take less than 37 minutes to complete the test.

Answer 1

0.0668 or 6.68%

Explanation:

Mean time (μ)= 46 minutes

Standard deviation (σ) = 6 minutes

The z-score for any given time X is determined by:

`z=(X-\mu)/(\sigma)`

For X = 37:

`z=(37-46)/(6)\\ z=-1.5`

A z-score of -1.5 corresponds to the 6.68th percentile of a normal distribution. The probability that it will take less than 37 minutes to complete the test is

`P(X\leq 37) = 0.0668=6.68\%`

The probability is 0.0668 or 6.68%