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 502 and the standard deviation is 116. Assume the variable x is normally distributed. left parenthesis a right parenthesis(a) What percent of the SAT verbal scores are less than 675? left parenthesis b right parenthesis(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575? left parenthesis a right parenthesis(a) Approximately nothing% of the SAT verbal scores are less than 675. (Round to two decimal places as needed.)

Explanation / Answer

A)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    675      
u = mean =    502      
          
s = standard deviation =    116      
          
Thus,          
          
z = (x - u) / s =    1.49137931      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.49137931   ) =    0.932069032 = 93.21% [answer]

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B)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    575      
u = mean =    502      
          
s = standard deviation =    116      
          
Thus,          
          
z = (x - u) / s =    0.629310345      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.629310345   ) =    0.26457295

We expect 0.26457295*1000 = 264.57295 or 265 [ANSWER]

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