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by **FWT** on Wed Mar 18, 2009 2:48 pm

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?

Please help as soon as possibel. thx

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by **stapel_eliz** on Sat Mar 21, 2009 9:56 pm

FWT wrote: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".

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

In your case, you have:

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

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!

by **FWT** on Sat Mar 28, 2009 9:39 pm

thanks i got it

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

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

Re: mean score 500, standard dev. 75, score in 75th percentile