Scores for men on the verbal portion of the SAT-I test are nor- mally distribute

Question

Scores for men on the verbal portion of the SAT-I test are nor- mally distributed with a mean of 509 and a standard deviation of 112.

(a) If 1 man is randomly selected, find the probability that his score is at least 571.

(b) If 17 men are randomly selected, find the probability that their mean score is at least 571.

17 randomly selected men were given a review course before taking the SAT test. If their mean score is 571, is there a strong evidence to support the claim that the course is actually effective?

(Answer yes or no)

Thank you.

Explanation / Answer

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    571      
u = mean =    509      
          
s = standard deviation =    112      
          
Thus,          
          
z = (x - u) / s =    0.553571429      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.553571429   ) =    0.289936092 [ANSWER]

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b)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    571      
u = mean =    509      
n = sample size =    17      
s = standard deviation =    112      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.282433471      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.282433471   ) =    0.011231881 [ANSWER]

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As this is a small probability, then YES, THE COURSE SEEMS TO BE EFFECTIVE. [ANSWER, YES]

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