The intelligence quotient (IQ) score, as measured by the Stanford-Binet IQ test, is normally distributed in a certain population of children. The mean IQ score is 100 points, and the standard deviation is 16 points. What percentage of children in the population have IQ scores

(i)140 or more,

(ii) 80 or less,

(iii) between 80 and 120,

(iv)between 80 and 140 and

(v) between 120 and 140?

Solution: (i) 0.0062 (ii) 0.1056, (iii)0.7888, (iv) 0.8882 , (v) 0.0994

Refer to the IQ distribution of the previous exercise. Let Y be the IQ score of a child chosen at random from the population. Find Pr(80 Y140).

Solution: 0.8882

Refer to the IQ distribution of the previous two exercises. Suppose five children are to be chosen at random from the population. Find the probability that exactly one them will

have an IQ score of 80 or less and four will have scores higher than 80. (HINT: First find the probability that a randomly chosen child will have an IQ score of 80 or less.)