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 between 85 and 115 .

The probability that a randomly selected adult has an IQ between 85 and 115 is? . ​

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

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 20

P(85 < x < 115) = P[(85 - 100)/ 20) < (x - ) /  < (115 - 100) / 20) ]

= P(-0.75 < z < 0.75)

= P(z < 0.75) - P(z < -0.75)

= 0.7734 - 0.2266

= 0.5468

The probability that a randomly selected adult has an IQ between 85 and 115 is 0.5468