Question

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P P (IQ greater than 95) = %

b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P P (IQ less than 125) = %

c) In a sample of 600 people, how many people would have an IQ less than 110? people d) In a sample of 600 people, how many people would have an IQ greater than 140? people

Answer 1

Solution :

Given that,

mean = = 100

standard deviation = = 15

a ) P (x > 95 )

= 1 - P (x < 95 )

= 1 - P ( x -  / ) < ( 95 - 100 / 15 )

= 1 - P ( z <- 5 / 15 )

= 1 - P ( z < - 0.33)

Using z table

= 1 - 0.3707

= 0.6293

Probability = 62.93%

c ) P (x > 125 )

= 1 - P (x < 125 )

= 1 - P ( x -  / ) < ( 125 - 100 / 15 )

= 1 - P ( z <  25 / 15 )

= 1 - P ( z < 1.67)

Using z table

= 1 - 0.9525

= 0.0475

Probability = 0.75%

c ) n = 600

P( X<  22 )

P ( x - /) < (110 - 100 /15)

P( z < 10 / 15 )

P ( z < 0.67 )   

Using z table

= 0.7389

Probability = 0.7389* 600 = 443

d ) P (x > 140 )

= 1 - P (x < 140 )

= 1 - P ( x -  / ) < ( 140 - 100 / 15 )

= 1 - P ( z < 40 / 15 )

= 1 - P ( z < 2.67)

Using z table

= 1 - 0.9962

= 0.0038

Probability = 0.0038* 600 = 2