Question

ACT scores are normally distributed and from 2015 to 2017, the mean was 20.9 with a standard deviation of 5.6.

To get accepted into OSU, you need at least a 27. What is the z-score you need to get accepted? Enter your answer, rounded to the nearest hundredth.

Answer 1

You need a z-score of at least 1.09 to get accepted.

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 question, we have that:

`\mu = 20.9, \sigma = 5.6`

To get accepted into OSU, you need at least a 27. What is the z-score you need to get accepted?

We need to find Z when X = 27. So

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

`Z = (27 - 20.9)/(5.6)`

`Z = 1.09`

You need a z-score of at least 1.09 to get accepted.