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Basic Question 1 of 7

The SAT scores of entering freshman at University X have a N(1200, 90) distribution. The SAT scores of entering freshman at University Y have a N(1215, 110) distribution. A random sample of 100 freshmen is taken from University X, and x-bar, the sample mean of the 100 scores from University X, is computed. The probability that x-bar is greater than 1215 is ______.

A. 0.0475
B. 0.5000
C. 0.4325

User Contributed Comments 11

User Comment
vincenthuang (1200-1215)/9=1.67--->z
check z table z(1.67)=.9525
P(x)=1-.9525=.0475
sivenkova Why 1200-1215 and why divided by 9, please?
capform 90 divided by square root of N (100)
surob Look at it this way:
(90^2/100)^(1/2)
JimM Without a z-table, 1.67 z-score (as vincenthuang showed) is real close to a 90% confidence interval (1.645). 5% lie above that interval, so answer A is correct.
boegs If a normal distribution is completely described by its mean and variance i.e. N(mean, variance), why do we not take the square-root of the variance (90) in the calculation of the standard error?
sgossett86 Yeah seriously! Shouldn't it be calculated 90^.5/100^.5 = .949 = sigma

and the z calculation should be 1215-1200.. but that isn't important.

i guess whatever. i get it in this context.
srdgreen Can someone please explain the N(1200,90) format?
raghu2gd Any normal distribution is denoted by N( Mean, variance). That means 1200 is mean and 90 is variance.
mzaheedihm Please check the solution of the next question. It is actually N (Mean, Standard Deviation)
chrismoore Concur with mzaheedihm - can we please verify the proper interpretation of N(1200,90)?
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Learning Outcome Statements

calculate and interpret the standard error of the sample mean;

CFA® 2024 Level I Curriculum, Volume 1, Module 5.