Question

The mean IQ score of adults is 100 , with a standard deviation of 15 . Use the Empirical Rule to find the percentage of adults with scores between 85 and 115 .

(Assume the data set has a bell-shaped distribution

Answer 1

Solution :

Given that ,

mean = =100

standard deviation = = 15

P(85< x <115) = P[(85 - 100) /15 < (x - ) / < (115 - 100 ) /15 )]

= P( -1< Z < 1)

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

using empirical rule

=68%/2 + 68%/2

=34%+34%

=68%