Math please help

Question

Given a normal distribution with a mean of 128 and a standard deviation of 15, what percentage of values is with an interval 83 to 173?

Answer 1

First, find the difference between the mean and the interval boundaries:

Upper boundary difference from mean = 173 - 128 = 45

Lower boundary difference deviation from mean = 128 - 83 = 45

So, both the lower and upper boundaries are 45 (in absolute value) away from our mean of 128. Now, we can divide each difference by our standard deviation of 15 to find the spread of our interval.

45/15 = 3 standard deviations, which means 99.7% of the values are captured by the given interval.

This problem is testing your knowledge of the 68, 95, 99.7 rule in statistics, which simply states:

68% of data falls within 1 standard deviation of the mean,

95% of the data falls within 2 standard deviations of the mean,

99.7% of the data falls within 3 standard deviations of the mean.