Question

2. Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 15. a. Sketch the distribution of Stanford–Binet IQ test scores. b. Write the equation that gives the z score corresponding to a Stanford–Binet IQ test score. Sketch the distribution of such z scores. c. Find the probability that a randomly selected person has an IQ test score i. Over 145. ii. Under 91

Answer 1

0.0010,0.2743

Explanation:

Given that Stanford–Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 15

If x represents the scores then

X is N(100,15)

a) See enclosed file

b) Z score =
`(x-100)/(15)`

c) the probability that a randomly selected person has an IQ test score

i. Over 145.

=
`P(X>145) = P(Z>3) = 0.0010`

ii. Under 91

=
`P(X<91) = P(Z<-0.6)\\= 0.2743`