The probability that a randomly selected adult has an IQ less than 132 is

Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. Find the probability that a randomly selected adult has an IQ less than 132.

Answer 1

The probability that a randomly selected adult has an IQ less than 132 is?

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. Find the probability that a randomly selected adult has an IQ less than 132.

In this question, you are asked to find the probability of an "individual" value from a given population, furthermore, the problem tells that it is "normally distributed."

(1) We will apply the "z-score" formulae to compute the z-value to look up probability in the z-table.

z =(X-μ)÷σ → z = (132 - 100) ÷ 20 = 32/20 → z = 1.6

(2) Find z = 1.6 on the z-score or normal distribution table of probability values, which yields the following answer as .9452 or 94.52%

(3) P(x < 132) or P(z < 1.6) = 94.52%