A set of test scores is normally distributed with a mean of 78 and a standard deviation of 4.5. Dwayne scored 87 on the test. What is his percentile score?

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A set of test scores is normally distributed with a mean of 78 and a standard deviation of 4.5. Dwayne scored 87 on the test. What is his percentile score?

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Answer 1 · 2017-06-11T01:34:22

$.9772$ $.9772$ or about $97.72 %$ $97.72%$

Explanation:

The question requires z-scores.

The formula is:

$z = \frac{x - μ}{σ}$ $z=(x-mu)/sigma$

Where $x =$ $x=$ the given value
$μ =$ $mu=$ the mean
$σ =$ $sigma=$ the standard deviation

Or

$z = \frac{your value - the actual mean}{S D}$ $z=("your value " - " the actual mean")/(SD)$

This is a bit easier to remember :)
(SD=Standard Deviation)

Plug in the values:

$z = \frac{87 - 78}{4.5}$ $z=(87-78)/(4.5)$

$z = 2$ $z=2$

Now you look up the probability that corresponds to the $z$ $z$ score in the table. (Which you should be provided with.)
The probability that corresponds to the $z$ $z$ score is $.9772$ $.9772$
All you have to do now is multiply by $100$ $100$ .

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A set of test scores is normally distributed with a mean of 78 and a standard deviation of 4.5. Dwayne scored 87 on the test. What is his percentile score?

1 Answer

Explanation:

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