Question

Intelligence Quotient​ (IQ) scores are normally distributed with a mean of 100 and a standard deviation of 15. If 9 people are randomly​ selected, what is the probability they will have a mean IQ score between 105 and ​110

Answer 1

Solution :

Given that ,

mean =   = 100

standard deviation = = 15  

n = 9

=100

=  / n= 15/ 9=5

P(105<     <110 ) = P[(105-100) / 5< ( - ) /   < (110-100) /5 )]

= P(1 < Z <2 )

= P(Z <2 ) - P(Z <1 )

Using z table

=0.9772-0.8413

=0.1359

probability= 0.1359