Question

length of time x to complete a particular college entrance test is normally distributed with an average of 125 minutes and a standard deviation of 18 minutes. What is the probability that a student taking this test will finish in 100 minutes or less

Answer 1

8.23% probability that a student taking this test will finish in 100 minutes or less

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 125, \sigma = 18`

What is the probability that a student taking this test will finish in 100 minutes or less

This is the pvalue of Z when X = 100. So

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

`Z = (100 - 125)/(18)`

`Z = -1.39`

`Z = -1.39` has a pvalue of 0.0823.

So there is an 8.23% probability that a student taking this test will finish in 100 minutes or less