Question

E09 Review

Scores on "The ability to do quantitative thinking" test are normally distributed with a mean of 250 and a standard deviation of
25. Brandi scored at the 81st percentile on this test. What was her test score?
is the test score for Brandi.

Answer 1

272 is the test score for Brandi.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 250 and standard deviation of 25:

This means that
`\mu = 250, \sigma = 25`

Brandi scored at the 81st percentile on this test. What was her test score?

The z-score of her score of X has a p-value of 0.81. This means that her score is given by X when Z = 0.88.

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

`0.88 = (X - 250)/(25)`

`X - 250 = 0.88*25`

`X = 272`

272 is the test score for Brandi.