Problems understanding how to calculate this problem. Can youhelp? Thank you. Qu

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Problems understanding how to calculate this problem. Can youhelp? Thank you. Question: The distribution of Wechsler Adult Intelligence Scale (IQTest) scores for persons over 16 years of age is approximatelyNormal with mean 100 and standard deviation 15. (a) What is the probability that a randomly chosen individualhas a WAIS score of 105 or higher? (b) What are the mean and standard deviation of the averageWAIS score x- for an SRS of 60 people? (c) What is the probability that the average WAIS score of anSRS of 60 people is 105 of higher? (d) Would the answers to any of (a), (b), or (c) be affectedif the distribution of WAIS scores in the adult population weredistinctly non-Normal? Problems understanding how to calculate this problem. Can youhelp? Thank you. Question: The distribution of Wechsler Adult Intelligence Scale (IQTest) scores for persons over 16 years of age is approximatelyNormal with mean 100 and standard deviation 15. (a) What is the probability that a randomly chosen individualhas a WAIS score of 105 or higher? (b) What are the mean and standard deviation of the averageWAIS score x- for an SRS of 60 people? (c) What is the probability that the average WAIS score of anSRS of 60 people is 105 of higher? (d) Would the answers to any of (a), (b), or (c) be affectedif the distribution of WAIS scores in the adult population weredistinctly non-Normal?

Explanation / Answer

X~Normal(=100, =15) (a) P(X>=105)=P((X-)/ >= (105-100)/15)=P(Z>=0.33) = 0.3707 (check normal table) (b) mean==100, standard deviation of 60=/sqrt(n)=15/sqrt(60)=1.936492 (c)P(x-bar >105)= P((x-bar - )/(/sqrt(n)) >(105-100)/(15/sqrt(60)) ) =P(Z>2.58) =0.0049 (check normaltable)

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