Question

The Wechsler IQ test are normally distributed with a mean 100 and a standard deviation of 15. If 23 randomly selected adults take the Wechsler IQ test, find the probability that their mean score is greater than 108. Round your probability to nearest hundreth of a percent.

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 15

n = 23

= 100

= / n = 15/ 23 = 3.13

P( >108 ) = 1 - P( <108 )

= 1 - P[( - ) / < (108-100) /3.13 ]

= 1 - P(z < 2.56)

Using z table

= 1 - 0.9948

=0.0052

probability= 0.0052

=0.52%