Question

r Intelligence Scale The Wechsler Intelligence Scale or Children is approximately normally distributed, with mean for 100 and standard deviation 15, a) What is the probability that a randomly selected test taker gra 15 the bel (b) What is the probability that a randomly selected test taker is e What proportion of test takers will score between 110 0 If a child is randomly selected, what is the probability that e What intelligence score will place a child in the 98th will score above 125? will score below 90? and 140? she scores above 150? percentile? Z-S 0 bormal intelligence is defined as scoring in the middle o of all test takers, figure out the scores that differentiate 95% ormal intelligence from abnormal intelligence.

Answer 1

(a)

Z for 125 will be

(125-100)/15 = 1.66666666667

P ( Z > 1.66666666667) = 0.047790352 { use the excel function =1-NORM.S.DIST(1.66666666667,TRUE)}

(b)

Z for 90

(90-100)/15 = -0.66666666666

P( Z < -0.66666666666) = 0.252492538 { Use the excel function =NORM.S.DIST(-0.66666666667,TRUE)}

(c)

Z for 110 is 0.666666666

Z for 140 = 40/15 = 2.666666

P ( 0.666666 < Z < 2.666666 ) = P ( Z < 2.66666666) - P(Z < 0.6666666) = 0.2487

(d) Z for 150 is

50/15 = 3.3333333

P ( Z > 3.33333) = 0.0004