Question

Problem Page Suppose that IQ scores in one region are normally distributed with a standard deviation of 15 . Suppose also that exactly 60% of the individuals from this region have IQ scores of greater than 100 (and that 40% do not). What is the mean IQ score for this region? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Answer 1

Solution:-

Given that,

x = 100

standard deviation = = 15

Using standard normal table,

P(Z < z) = 60%

= P(Z < z) = 0.60  

= P(Z < 0.2534 ) = 0.60

z = 0.2534

Using z-score formula,

x = z * +

100 = 0.2534 * 15 +

= 100 - 3.801

= 96.2