- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 7. Estimation and Inference
- Subject 2. The Central Limit Theorem and Inference
CFA Practice Question
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 ______.
B. 0.5000
C. 0.4325
A. 0.0475
B. 0.5000
C. 0.4325
Correct Answer: A
x-bar has a N(1200, 90/1001/2) distribution. You now need to evaluate P(x-bar > 1215). The result is 0.0475.
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)? |