Question

A high school track team has a grade point average of 3.36, with a standard deviation of 1.2. Their coach wants to identify the team members in the bottom 33% for extra tutoring help. What is the grade point average that will mean that a track team athlete will be recommended for extra tutoring help if the coach examines just 32 of her athletes

Answer 1

GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help

Explanation:

When the distribution is normal, we use 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 question:

`\mu = 3.36, \sigma = 1.2`

Bottom 33%:

The 33rd percentile(X when Z has a pvalue of 0.33) and below.

So we have to find X when Z = -0.44.

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

`-0.44 = (X - 3.36)/(1.2)`

`X - 3.36 = -0.44*1.2`

`X = 2.832`

GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help