The Wechsler Adult Intelligence Scale (WAIS) is a common \"IQ test\"for adults.

Question

The Wechsler Adult Intelligence Scale (WAIS) is a common "IQ test"for adults. The distribution of WAIS scores for persons over 16years of age is approximately Normal with mean 100 and standarddeviation 15.

(a) What is the probability that a randomly chosen individual has aWAIS score of 105 or higher?

(b) What are the mean and standard deviation of the average WAISscore xbar for an SRS of 60 people?

(c) What is the probability that the average WAIS score of an SRSof 60 people is 105 or higher?

(d) Would your answer to any of a, b, c be affected if thedistribution of WAIS scores in the adult population were distinctlynon-Normal?
So in (a) I looked for the z score and ended up with 0.0005 becauseof N(100, 1.5). In (b) I did =np and=np(1-p). For (c) I found the z score to be 4000 and Idon't know where I went wrong.

Explanation / Answer

I believe you were assuming that the scores werebinomial and you were using a normal approximation. That isnot our case here. We are given the scores are normalN(=100,=15). (a)P(X>=105)=1-P(X<105)=1-P{Z<(105-100)/15}=1-P(Z<1/3)=.369441 (b)Now the radom variable is Xbar with n=60. ThereforeXbar is N(100,15/60) (c)P(Xbar>=105)=1-P(Xbar<105)=P{Z<(105-100)/(15/60)}=.004912 (d)Parts b and c would not change because Xbar will benormally distributed by the central limit theoren. For asample of size 60 the approximation would be excellent. Now part a could indeed be wrong if X values were not normaland skewed in any direction.

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