Part C WITHOUT using a table only a calculator The distribut

The distribution of scores for persons over 16 years of age on the Wechler Adutt Intelligence Scale (WAIS) is approximately normal with mean 100 and standard deviation 15. The \"WAIS\" is one of the most common 70 Tests\' for adults. What is the probability that a randomly chosen individual has a WAIS score of 105 or higher? ~ What are the mean and standard deviation of the average WAIS score x for a SRS of 60 people What is the probability that the average WAIS score of an SRS of 60 people is 105 or higher Would your answers to any of , , or be affected if the distribution of WAIS scores in the adult population were distinctly non-normal

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    105      
u = mean =    100      
n = sample size =    60      
s = standard deviation =    15      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.581988897      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.581988897   ) =    0.004911637 [ANSWER]

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If you have a ti-84, you can use NORMCDF(2.5819888, 1E99, 0, 1) to get the right tailed area of our z score here. Thanks!