Question

Question #b5806

Answer 1

`=97.72%`

Explanation:

To find the area under a bell curve, which is equivalent to finding the percentage, we use this formula:
`z=(x-mu)/sigma`, where `z` is the number of deviations away from the mean a score is, `x` is the score, `mu` is the mean and `sigma` is the standard deviation.

Since the question already gives us the score, mean and standard deviation, we plug them into the formula to get:
`z= (78-84)/3`

`z=-6/3`

`z=-2`. From here we look up a z-score table for the left of curve to find that `97.72%` of the area of the bell curve is above 78, which means `97.72%` of tests scored better then 78.

http://www.statisticshowto.com/probability-and-statistics/z-score/

I hope I helped!