- CFA Exams
- CFA Exam: Level I 2021
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 8. The Standard Normal Distribution

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**CFA Practice Question**

The daily sales at a certain cafe follow a normal distribution with a mean of $1,060 and a standard deviation of $310. What is the probability that the daily sales are between $471 and $1,401?

B. 0.3643

C. 0.8356

A. 0.4713

B. 0.3643

C. 0.8356

Correct Answer: C

The z-value corresponding to $1,401 is computed as: z = (1401 - 1060)/310 = 1.10, and P(Z<= 1.10) = 0.8643.

The probability that sales are between $471 and $1,401 is the difference in the cumulative probability values: 0.8643 - 0.0287 = 0.8356.

The z-value corresponding to $471 is computed as: z = (471 - 1060)/310 = -1.90, and P(Z<= -1.90) = 0.0287.

The z-value corresponding to $1,401 is computed as: z = (1401 - 1060)/310 = 1.10, and P(Z<= 1.10) = 0.8643.

The probability that sales are between $471 and $1,401 is the difference in the cumulative probability values: 0.8643 - 0.0287 = 0.8356.

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**User Contributed Comments**
3

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

StanleyMo |
for P (Z<1.1 ) = 68% While P (Z<-1.9 ) similar to Z<-1.96 which <5%, so it would be equal 50% + 34.13% - <5% = <84.13%, so result is 0.8356 |

chamad |
StanleyMo! Where did you get the 68% from? is it the empirical rule? |

tschorsch |
since the range is more than 1 std dev below to more than 1 std dev above, the P(interval) must be > 68%, so C must be it |