IQ scores are designed to have a mean of 100 and a standard

IQ scores are designed to have a mean of 100 and a standard deviation of 15. IQ testing is one way on which people are categorized as having different levels of metal disability; there are four levels of mental retardation between the IQ scores of 0 and 70.

B. Must show work: People with IQ scores of 50-75 have scores in the topmost category of IQ scores that indicate an impairment. They are said to hve mild mental retardation. They can attain as high as a sixth-grade education and are often self - sufficient, what percent fall into this range?

Solution

= 100
= 15
standardize x to z = (x - ) /
P( 50 < x < 75) = P[( 50 - 100) / 15 < Z < ( 75 - 100) / 15]
P( -3.3333 < Z < -1.6667) = 0.0475 - 0.000429 = 0.04707 = 4.7 percent
(From Normal probability table)