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
Marvin V.
Jun 11, 2017

#.9772# or about #97.72%#

Explanation:

The question requires z-scores.

The formula is:

#z=(x-mu)/sigma#

Where #x=#the given value
#mu=# the mean
#sigma=# the standard deviation

Or

#z=("your value " - " the actual mean")/(SD)#

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

Plug in the values:

#z=(87-78)/(4.5)#

#z=2#

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

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