Question 17) The Wechsler Adult Intelligence Scale (WAIS) is a common \"IQ test\

Question

Question 17)The Wechsler Adult Intelligence Scale (WAIS) is a common "IQ test" for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 94 and standard deviation 16.

a. The mean value of x¯¯¯x¯ for an SRS of 55 people is .

b. The standard deviation of x¯¯¯x¯ (±± 0.01) for an SRS of 55 people is .

c. The z-score (±± 0.01) corresponding to an average WAIS score of 96 for an SRS of 55 people is .

d. What is the probability (±± 0.0001) that the average WAIS score of an SRS of 55 people is 96 or higher?

Explanation / Answer

= 94

= 16

a) mean value of x¯ = = 94

b) standard deviation of x¯ = / sqrt(n) = 16 / sqrt(55) = 2.16

c) Z score for a score of 96 for an SRS of 55 people = (96 - 94) / 2.16 = 0.93

d) P( x¯ > 96) = P(Z > 0.93)

                        = 1 - P(Z < 0.93)

                        = 1 - 0.8238

                        = 0.1762

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