Question

IQ scores in a certain population are normally distributed with a mean of 101 and a standard deviation of 13. (Give your answers correct to four decimal places.) (a) Find the probability that a randomly selected person will have an IQ score between 99 and 108. (b) Find the probability that a randomly selected person will have an IQ score above 89

Answer 1

Solution :

Given that ,

mean = = 101

standard deviation = =13

P(99< x < 108) = P[(99-101) / 13< (x - ) / < (108-101) /13 )]

= P( -0.15< Z <0.54 )

= P(Z < 0.54) - P(Z < -0.15)

Using z table   

=  0.7054 - 0.4404

probability= 0.2650

b.

P(x >89 ) = 1 - P(x<89 )

= 1 - P[(x -) / < (89-101) /13 ]

= 1 - P(z <-0.92 )

Using z table

= 1 -  0.1788

probability= 0.8212