- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 6. Measures of Dispersion

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**CFA Practice Question**

For x, a normal random variable with mean = 70 and standard deviation = 10, what x-score is 1.2 standard deviations below the mean?

B. 58

C. 68.8

A. 82

B. 58

C. 68.8

Correct Answer: B

The mean minus 1.2 standard deviations is 70 - 1.2(10) = 70 - 12 = 58.

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**User Contributed Comments**
6

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

bentang |
can someone explain the formula? |

bobert |
The highest point on the normal distribution is the mean, therefore the middle. 1 standard deviation is going to be +/- 10. The question asks for 1.2 standard deviations BELOW the mean. Because it is below we are going to be subtracting, and since 1 standard deviation = 10, 1.2 = 12. This leaves us with 70 - 12 = 58. |

JKiro |
1st note: this is a normal distribution mean of 70 & std dev. of 10--> 1 std dev. (given) looking for value of x to result in 1.2 std dev (1.2/1)(10) = 12 is the resultant shift from the mean (positive or negative) given a 1.2 std dev. for negavite shift (below): x = 70 - 12 --> 58 for positive shift (above): x = 70 + 12 --> 82 the question asked for the value of x (from the mean) below: 58 |

tschorsch |
I think that the distribution is irrelevant for this question. 1.2 std devs below the mean should always be mean - 1.2 x stddev |

peteSP |
mean / 1.2 = 58 |

2014 |
Pete what if they ask above 58 would be wrong |