Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
A) If one person are randomly selected, find the probability the IQ score is greater than 112.
B)If one person are randomly selected, find the probability the IQ score is less than 95.
C)If one person are randomly selected, find the probability the IQ score is between 97 and 110.
D) If 16 people are randomly selected, find the probability the IQ score will be less than 95.

Answer 1

Solution:

Given that,

mean = = 100

standard deviation = = 15

A ) p ( x > 122 )

= 1 - p (x < 12.4 )

= 1 - p ( x -  / ) < ( 122 - 100 / 15)

= 1 - p ( z < 22 / 15 )

= 1 - p ( z < 1.47)

Using z table

= 1 - 0.9292

= 0.0708

Probability = 0.0708

B ) p ( x < 95 )

= p ( x -  / ) < ( 95 - 100 / 15)

= p ( z < - 5 / 15 )

= p ( z < -0.33 )

Using z table

= 0.3707

Probability = 0.3707

C ) p ( 97 < x < 110 )

= p ( 97 - 100 / 15) < ( x -  / ) < ( 110 - 100 / 15)

= p ( - 3 / 15 < z < 10 / 15 )

= p (- 0.2 < z <0.67 )

= p (z < 0.67 ) - p ( z < - 0.2 )

Using z table

= 0.7486 - 0.4207

= 0.3279

Probability = 0.3279

D ) n = 16

So,

   = 100

=  ( /n) = (15 / 16 ) = 3.75

p (   < 95 )

= p ( - /) < (95 - 100 / 3.75)

= p ( z < - 5 / 3.75 )

= p ( z < -1.33 )

Using z table

= 0.0918

Probability = 0.0918