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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 ______.
B. 0.5000
C. 0.4325
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)? |
I am using your study notes and I know of at least 5 other friends of mine who used it and passed the exam last Dec. Keep up your great work!
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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.