MHB What percentage of the class scored between a 67% and an 83%

[anyalong18]

The exam scores for a particularly difficult math test had a mean score of 75% with a standard deviation of 8%. Approximately what percentage of the class scored between a 67% and an 83%.

 

[Prove It]

Assuming this is a normal distribution, these scores are each within one standard deviation from the mean, so the percentage is...?

 

[HOI]

I'm sure you know, if you are taking a course in which a question like this is asked, that you do NOT "calculate" the answer but look it up in a table of the "Standard Normal Distributio". Surely there must be one in your textbook but there are also several on line.

There is a good one at normal distribution table - Bing images

The standard normal distribution has mean 0 and standard deviation 1. With mean 75 and standard distribution 8, (x- 75)/8 corresponds to x.

So a score of 67 corresponds to (67- 75)/8=-8/8= -1 and a score of 83 corresponds to (83- 75)/8= 8/8= 1.

Those scores are, as Prove It said, one standard deviation off the mean. In the table, you look up z= 1 and, because of the symmetry, the "z-score" for -1 is the negative of that. x- (-x)= 2x so the probability is just 2 times the value you looked up.