Question

Adults have a IQ scores that are normally distributed with a mean of a 100 and a standard deviation of 15.

a) what percentage of scores are less than 103?

b) what percentage of scores are between 60 and 130?

c) what is the IQ score seperating the bottom 25% from the rest?

thank you.

Answer 1

Given,

= 100 , = 15

We convert this to standard normal as

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

a)

P( X < 103) = P( Z < 103 - 100 / 15)

= P( Z < 0.2)

= 0.5793

b) .

P( 60 < X < 130) = P( X < 130) - P( X < 60)

= P( Z < 130 - 100 / 15) - P( Z < 60 - 100 / 15)

= P( Z < 2) - P( Z < -2.6667)

= 0.9772 - 0.0038

= 0.9734

c)

We have to calculate x such that

P( X < x) = 0.25

That is

P( Z < x - / ) = 0.25

From Z table, z-score for the probability of 0.25 is -0.6745

x - / = -0.6745

x - 100 / 15 = -0.6745

x = 89.8825