Scores for men on the verbal portion of the SAT-I test are normally distributed

Question

Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 586.5, is there a strong evidence to support the claim that the course is actually effective? (Enter YES or NO) 20 randomly selected men were given a review course before taking the SAT test. If their mean score is 586.5. 20 men are randomly selected, find the probability that their mean score is at least If 586.5. (b) 1 man is randomly selected, find the probability that his score is at least If 112. (a) 509 and a standard deviation of

Explanation / Answer

Normal Distribution
Mean ( u ) =509
Standard Deviation ( sd )=112
Normal Distribution = Z= X- u / sd ~ N(0,1)  
a)
P(X < 586.5) = (586.5-509)/112
= 77.5/112= 0.692
= P ( Z <0.692) From Standard Normal Table
= 0.7555                  
              
P(X > = 586.5) = (1 - P(X < 586.5)
= 1 - 0.7555 = 0.2445                  
b)
P(X < 586.5) =   (586.5-509)/112/ Sqrt ( 20 )
= 77.5/25.044= 3.0946
= P ( Z <3.0946) From Standard NOrmal Table
= 0.999                  
P(X > = 586.5) = 1 - P(X < 586.5)
= 1 - 0.999 = 0.001                  
c)
No

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