Question

# Use the normal distribution of SAT critical reading scores for which the mean is 507507 and...

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

507507

and the standard deviation is

108108.

Assume the variable x is normally distributed.

 left parenthesis a right parenthesis(a) What percent of the SAT verbal scores are less than 650650​? left parenthesis b right parenthesis(b) If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 575575​?

left parenthesis a right parenthesis(a)

Approximately

1.341.34​%

of the SAT verbal scores are less than

650650.

​(Round to two decimal places as​ needed.)

left parenthesis b right parenthesis(b)

You would expect that approximately

1.321.32

SAT verbal scores would be greater than

575575.

​(Round to the nearest whole number as​ needed.)

 for normal distribution z score =(X-μ)/σx here mean=       μ= 507 std deviation   =σ= 108.000

a)

 probability =P(X<650)=(Z<(650-507)/108)=P(Z<1.32)=0.9073 ~ 90.73 %

Approximately  90.73 % of the SAT verbal scores are less than 650.

2)

 probability =P(X>575)=P(Z>(575-507)/108)=P(Z>0.63)=1-P(Z<0.63)=1-0.7355=0.2645

You would expect that approximately 1000*0.2645 ~ 265 SAT verbal scores would be greater than 575.

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