Use the normal distribution bell curve.

The mean for a set of scores is 100 and the standard deviation is 7.5. Find the probability that a randomly selected score is between

a. 85 and 100.

b. between 85 and 115

c. less than 100

The IQ test scores are Normally distributed with mean 100 and standard deviation 15.

Let X be the IQ test score of person.

We have to find the probability that person would score between 85 and 115 is

P (85 < X < 115) =

= P (-1 < Z < 1)

= P (Z < 1) - P (Z < - 1)

= 0.8413 - 0.1587

P (85 < X < 115) = 0.6826

The probability that a person would score between 85 and 115 is 0.6826