Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals μ=105 and a standard deviation sigma equals σ=15. Find the probability that a randomly selected adult has an IQ between 95 and 115.

Answer 1

µ = 105, σ = 15

Probability that a randomly selected adult has an IQ between 95 and 115 =

= P(   95   < X <   115   )                              
= P( [(   95   -   105   )/   15   ] < (X-µ)/σ < [(   115   -   105   )/   15   ])
= P(   -0.6667   < z <   0.6667   )                              
= P( z <   0.6667   ) - P( z <     -0.6667   )                          
Using excel function:                                              
= NORM.S.DIST(   0.6667   ,1) - NORM.S.DIST(       -0.6667   ,1)                          
= 0.4950