- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 10. Sampling and Estimation
- Subject 6. Confidence Intervals for the Population Mean

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**CFA Practice Question**

A client will move his investment account unless the portfolio manager earns at least a 10 percent rate of return on the account. The rate of return for the portfolio the portfolio manager has chosen has a normal probability distribution with an expected return of 19 percent and a standard deviation of 4.5 percent. What is the probability that the portfolio manager will keep this account?

A. 0.950

B. 1.000

C. 0.975

**Explanation:**As a rule of thumb, two standard deviations produce a 95% confidence level. Since this question presents a one-tailed test, the probability of falling below the expected value by two standard deviations is 2.5%.

Confidence interval = (19% - 10%)/4.5% = 2 standard deviations

The frequency of outcomes two standard deviations less than the expected return is 2.28%.

Hence, the probability of keeping the account = 1.0000 - 0.0228 = 0.9772, closest to 0.975.

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**User Contributed Comments**
3

User |
Comment |
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tenny45 |
since it's a one-tailed test, isn't the probability of falling below the expected value by two std. dev. 5% (instead of 2.5%)? Also, how do you get 0.0228 w/o the z chart? |

whoi |
no, confidence interval is never one-sided ;) |

boddunah |
is it not SFratio question. minimum accecptable level 10%. E(R)= 19%. sigma = 4.5. 19-10/4.5 = 2.probability of falling below minimum acceptable level = 1-N(2).but asking for "keeping the account" means return above minimum threshold level.which is N(2)= z- table gives 0.9772. |