z-score is a statistical tool that is used to estimate the probability of finding a number in a normal distribution of data. A normal distribution is described as a function in which the mean is zero, the standard deviation is 1 and that the area under the curve is equal to 1.
The z-score at 86 is z = (86-80)/6 = 1. the probability to the right is 0.1587.
The z-score at 92 is z = (92-80)/6 = 2. the probability to the left is 0.9772.
The difference in probability is equal to 0.8185. We multiply this to the number of total students to get the answer.
