Melissa P. answered • 10/16/14

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In order to find normal distribution, you need to figure out the z-score:

score - mean

_______________ = z-score

standard deviaton

Lets start with the z-score of 56:

56-70 -4

_____ = ____ ≈ -0.57

7 7

Next look up -0.57 on the Negative z-scores chart for Normal Distribution, which is .2843

Lets leave that for now because we need to find the z score for 77 now:

77-70 7

_____ = ____ = 1.0

7 7

Look up 1.0 on the Positive z-scores chart for Normal Distribution, which is .8413

Now take .8413 and subtract it from .2843

.8413

-.2843

______

.5570

To get percent, just multiply your answer by 100:

.5570 x 100 = 55.7% -- therefore, 55.7% of scores were between 56 and 77.