Question

Assume that adults have IQ scores that are normally distributed with a mean of 200 and a standard deviation of 20. Find the probability that a randomly selected adult has an IQ between 150 and 175.

Answer 1

Given,

= 200 , = 20

We convert this to standard normal as

P( X < x) = P (Z < x - / )

So,

P(150 < X < 175) = P( X < 175) - P( X < 150)

= P( Z < 175 - 200 / 20) - P( Z < 150 - 200 / 20)

= P( Z < -1.25) - P( Z < -2.5)

= ( 1 - P (Z < 1.25) ) - ( 1 - P( Z < 2.5) )

= ( 1 - 0.8944) - P( 1 - 0.9938) (Probability calculated from Z table)

= 0.0994