Question

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.)  

Answer 1

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.