Use the normal distribution of SAT critical reading scores for which the mean is

Question

Use the normal distribution of SAT critical reading scores for which the mean is 501 and the standard deviation is 109 . Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 600 ?

(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525 ?

(a) Approximately ____% of the SAT verbal scores are less than 600 . (Round to two decimal places as needed.)

(b) You would expect that approximately ____SAT verbal scores would be greater than 525 . (Round to the nearest whole number as needed.)

Explanation / Answer

Mean ( u ) =509
Standard Deviation ( sd )=109
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a.
P(X < 600) = (600-509)/109
= 91/109= 0.8349
= P ( Z <0.8349) From Standard Normal Table
= 0.7981  
Approximately 79.81% ~ 80% of the SAT verbal scores are less than 600
              
b.
P(X > 525) = (525-509)/109/ Sqrt ( 100 )
= 16/10.9= 1.4679
= P ( Z >1.4679) From Standard Normal Table
= 0.0711                  
would expect that approximately 7.11 ~ 7% SAT verbal scores would be greater than 525

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