Use the normal distribution of SAT critical reading scores for which the mean is 514and the standard deviation is108. Assume the variable x is normally distributed. What percent of the SAT verbal scores are less than600600​? If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than575575​?

Question
Asked Dec 16, 2019
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Use the normal distribution of SAT critical reading scores for which the mean is 514and the standard deviation is
108. Assume the variable x is normally distributed.

 
What percent of the SAT verbal scores are less than
600600​?
 
If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than
575575​?
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Expert Answer

Step 1

Given data normally distributed with mean of 514 and standard deviation of 108.

Let ‘X’ be a normal distribution random variable.

Step 2

Now, percent of the SAT verbal scores are less than 600 is,

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X-u 600-514 P(X<600) =P 108 =P(Z<0.7962962963) - P(Z<0.80) From standard normal table, P(X<600) =0.78814 P(X<600) = 0.7881 P(X<600)= 78.81%

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Step 3

Therefore, required percent of the SAT verbal scores...

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