Question #58874

1 Answer
Marvin V.
Jun 11, 2017

#.6826xx500=341.3# Or about #342# students

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=(76-82)/(6)# #&# #z=(88-82)/(6)#

#z=-1# #&# #z=1#

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 each #z# score respectfully is #.1587# #&# #.8413#

You subtract #.8413# from #.1587# because we want to find out the scores in between these two.
Which is #.6826#
All you have to do now is multiply by #500#.

Below is a picture that illustrates the concept better:

enter image source here

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