Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 105 and a standard deviation of 14. Using the empirical rule, what percentage of IQ scores are at least 77 ? Please do not round your answer.

Answer 1

Given,

= 105 , = 14

z = (x - ) /

= ( 77 - 105 ) / 14

= -2

That is 77 is 2 standard deviation below the mean.

Using empirical rule, approximately, 95% of the data falls in 2 standard deviation of the mean.

That is 5% of the data falls outside the 2 standard deviation and 2.5% falls either side of outside region.

P(X >= 77) = 95 + 2.5 = 97.5%