- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 6. The Normal Distribution

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**CFA Practice Question**

For x, a normal random variable, which of the following is false?

B. Q1 is 0.67 standard deviations below the mean.

C. x-score that cuts off the top 10% of the distribution is 1.28 standard deviations below the mean.

A. P(Q1 < x < Q3) = 50%

B. Q1 is 0.67 standard deviations below the mean.

C. x-score that cuts off the top 10% of the distribution is 1.28 standard deviations below the mean.

Correct Answer: C

The x-score that cuts off the top 10% of the distribution must be above the mean. In fact, the x-score that cuts off the top 10% of the distribution is 1.28 standard deviations above the mean.

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**User Contributed Comments**
11

User |
Comment |
---|---|

tenny45 |
Can someone explain how to get the st.dev of 1.28? |

tanyak |
Confidence interval for the 90th percentile (top 10%) for normal random variable is 1.282. 1.282 is just a number you need to know as it is stated in the text. 95th percentile - 1.65 99th percentile - 2.327 I would memorize these just in case... |

sivenkova |
Why are confidence interval stated differently: in the text it is said 90% - 1.645, not 1.282? |

rickeling |
1.282 is the square root of 1.645 |

surob |
Rickeling, I don't agree with you. I think you cannot take square root of 1.645 because: 1) it is not a varian to take a square root; 2) it simply serves as a multiplier for a standard deviation such as 1.645*standard deviation +/-mean - 90% confidence interval I think the question is implying that 80% of the x lies within 1.28*s +/-mean. 10% - upper tail of the normal distribution, 10% - lower tail of the normal distribution. |

mordja |
Not to point out the obvious but we know that 50% of the distribution lies above the mean. If a score is below the mean, we know it cuts off >10% of the distribution. The last answer is obviously wrong without needing to calculate. |

MFTIOA |
+- 1.28 =80% +- 1.65 =90% +- 1.96 =95% +- 2.58 =99% +- 1.00 =68% |

TheHTrader |
And how do you explain "Q1 is 0.67 standard deviations below the mean"? |

ngoldstein |
Quartile 1 is 0.67 Standard deviations below the mean. Theres no way they don't include a z-table, t-table, chi-square and f-table (if they are required), right? |

DonAnd |
+-(0.67)s.d. = 50% |

davcer |
99 - 2.58 98- 2.33 95- 1.96 90- 1.65 80- 1.28 |