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

Question

The Wechler 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 100 and standard deviation 15. Use this information to answer the following questions. What score places a randomly selected individual in the 95^th percentile? Describe the sampling distribution of the average WAIS score for an SRS of GO people? What is the probability that the average WAIS score of a SRS of 60 people is at least 105?

Explanation / Answer

1) here as we get from normal value table for 95% ; z=1.6449

hence corresponding value =mean +z*Std deviaiton =100+1.6449*15=124.67

2) for sample size 60,. distribution will be approximatley normal with mean =100

and std error =std deviation/(n)1/2 =1.9365

3)P(X>105) =1-P(X<105)=1-P(Z<(105-100)/1.9365)=1-P(Z<2.582)=1-0.9951=0.0049

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