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) = [tex] P(\frac{85-100}{15} < \frac{x-mean}{standard deviation} < \frac{115-100}{15} ) [/tex]
= 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
