Assume that adults have IQ scores that are normally distribu

Assume that adults have IQ scores that are normally distributed with a mean of ?=100 and a standard deviation ?=20. Find the probability that a randomly selected adult has an IQ less than 140.

The probability that a randomly selected adult has an IQ less than 140 is?______

(Type an integer or decimal rounded to four decimal places as needed.)

Solution

68% of all adults will have an IQ within 1 standard deviation of the mean (between 100 - 20 = 80 and 100 + 20 = 120). Since the IQ scores are normally distributed, it is equally likely to have an IQ of between 80 and 100 as it is to have an IQ of between 100 and 120, so 68/2 = 34% of all adults have an IQ of between 100 and 140. Then, due to the symmetry of the bell curve, 50% of all adults will have an IQ of less than 100 (since 100 is the mean), so the required probability is 50 + 34 = 84%.

Alternatively, you can use a z-table to compute:
P(x < 140) = P(z < (140 - 100)/30) = P((z < or = 2)).