For a standardized psychology examination intended for psychology majors, the hi

Question

For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 500 and a standard deviation of 175. The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 528. What is the probability that a sample of 40 exams will have a mean score of 528 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    528      
u = mean =    500      
n = sample size =    40      
s = standard deviation =    175      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.011928851      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.011928851   ) =    0.155786037 [ANSWER]

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