- CFA Exams
- CFA Level I Exam
- 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 seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing between 13 and 16 pounds?

A. 118

B. 100

C. 197

**Explanation:**[z = (x-u)/σ. z

_{1}= (13 - 15)/1.75 = -1.1429 and z

_{2}= (16 - 15)/1.75 = 0.5714]

The respective areas for those z-values are 0.3729 and 0.2157. Since they are on opposite sides of the mean, we add them to find the area in between, which is 0.5886. Therefore, 0.5886*200 = 118.

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**User Contributed Comments**
8

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

gambary |
again, z table? are we going to have those on the exam? |

danlan |
Area between -1.1429 and 0.5714 should be a value greater than 0.5 and smaller than 1, so the number of peppers should be between 100 and 200. 197 is too close to 200, and only 118 is reasonable. |

kevinf12 |
Actually, another way to get close is to break it into a few parts. First, say that 13.25 is 1 Std Dev away to the left. And within one Std Deviation is 68% (136 people). Then take 1/2 of that to estimate the amount in between 13.25 to 15 (this approximates how many are in the left side). Then, do a similar function for the right side. I chose 1/2 Std deviation which is 15.875. Within this is 50% (100 people). Of those 100 people, 50 lie to in between 15 to 15.875. So this gets 118. |

jerylewis |
good reasoning kevin |

zzhumanov |
explain me pls, how Z1 = -1.1429 and z2 = 0.5714 equal to 0.3729 and 0.2157. I could find this amounts in z table. thanks |

Harunoame |
zzhumanov. Z1=-1.1429 have a probability 1-.8729=.1271 Z2=.5714 have a probability 1-.7157=.2843 P=.1271+.2843=.4114 if we are finding the probability of "corns that is SMALLER then 13 and LARGER then 16" we use .4114*200 = 82.28 However the question is asking the probability of "corns that fall within 13 and 16", so we use 1-.4114=.5886 If you draw a graph with shaded areas for the z-value and the probability it represent, you will understand |

GBolt93 |
Another way is to think 1.14z is at least .34 and to the right if you multiple (1/1.75)*.34 you get .194, which you know more is conservative since it's more concentrated closer towards the mean. Therefore it's atleast .34+.194=53% which is greater than 100. |

Sheeb |
Here's what I did, STD = 1.75 right? So we know 68% of values lie within 1 STD. So as a best guess .68*200=136. The answer that was closest to 136 was 118. |