Question

According to a recent study, the average IQ in a population is 100 with standard deviation 15

(a) What is the probability that a randomly selected group of 100 people has an average IQ above 115?

(b) What is the probability that a randomly selected group of 100 people has an average IQ above 110 and below 90?

Answer 1

Solution :

Given that ,

a) P(x > 115) = 1 - p( x< 115)

=1- p P[(x - ) / < (115 - 100) / 15]

=1- P(z < 1.00)

= 1 - 0.8413

= 0.1587

b) P(90 < x < 110 )

= P (90 - 100) / 15) < P(x - ) / < (110 - 100) / 15]

= P( -0.67 < z < 0.67 )

=P(z < 0.67) - P(z < -0.67)

= 0.7486 - 0.2514

= 0.4972