## mean score 500, standard dev. 75, score in 75th percentile

Standard deviation, mean, variance, z-scores, t-tests, etc.
FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### mean score 500, standard dev. 75, score in 75th percentile

The mean score on a certain standardized test is 500, with a standard deviation on 75. Jessie scored in the 75th percentile. What was Jessie's score and the z score?

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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The mean score on a certain standardized test is 500, with a standard deviation on 75. Jessie scored in the 75th percentile. What was Jessie's score and the z score?
They should have given you some sort of formula for converting between z-score and the mean "mu" and standard deviation "sigma".

. . . . .$z\, =\, \frac{X\, -\, \mu}{\sigma}$

. . . . .$z\, =\, \frac{X\, -\, 500}{75}$

A score in the 75th percentile represents a score which is greater than 75% of all of the scores. With respect to the standard-normal curve, it represents the probability that a given score Z will be in the lower 75% of the scores: P(Z < z) = 0.75. Depending on the table (or calculator) you're using, this value will be something close to 0.674. Then:

. . . . .$0.674\, =\, \frac{X\, -\, 500}{75}$

Solve this for Jessie's score X.

Hope that helps!

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

thanks i got it