Question

Question #58874

Answer 1

`.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: