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Basic Question 5 of 11
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 used your notes and passed ... highly recommended!
Lauren
Learning Outcome Statements
explain the central limit theorem and its importance for the distribution and standard error of the sample mean
CFA® 2024 Level I Curriculum, Volume 1, Module 7.