Assume that adults have IQ scores that are normally distribu

Assume that adults have IQ scores that are normally distributed with a mean of 105 and a standard deviation 15. Find P₂, which is the IQ score separating the bottom 2% from the top 98%.

The IQ score that separates the bottom 2% from the top 98% is P₂₌ _____

(Round to the nearest hundredth as needed.)

Solution

P(X<c)=0.02

--> P((X-mean)/s <(c-105)/15) = 0.02

--> P(Z<(c-105)/15) = 0.02

--> (c-105)/15= -2.05 (from standard normal table)

So c= 105-2.05*15 =74.250