- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 5. Sampling and Estimation
- Subject 5. Confidence Intervals for the Population Mean and Selection of Sample Size

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**CFA Practice Question**

In estimating the population proportion for the days in summer that have thunderstorms, p, if the sample proportion, p', is 0.35 and the sample size is n = 92, the standard deviation of the sampling distribution is ______ (to nearest 0.001).

B. 0.350

C. 0.050

A. 0.650

B. 0.350

C. 0.050

Correct Answer: C

For a proportion the standard deviation of the sampling distribution, the distribution of the p's is shown at top right. Working with this formula, we get 0.050.

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**User Contributed Comments**
7

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

Pieter |
Where does this formula come from? |

savita |
binomial distribution. The variance is p(1 - p). |

StanleyMo |
excuse me, variance = P(1-p)/n under this situation. |

apiccion |
Savita, variance of a binomial distribution is np(1-p). You're thinking of a Beroulli random variable. |

cleopatraliao |
sampling distribution dealing with mean so we have to divide by n but not binomial, this is different. Just google the difference |

johntan1979 |
http://www.stat.yale.edu/Courses/1997-98/101/binom.htm pop mean, var = np, np(1-p) sample mean, var = p, [p(1-p)]/n Too easy to assume sample var is divided by only one n to become p(1-p) like the mean. |

sgossett86 |
Without reading above... CFAs this was like the last question which i commented on. We saw that sd=(p(1-p))^.5 ... remember that we're finding the sd of the SAMPLING DISTRIBUTION, so we have to plug that into the standard error formula sd/N^.5 that'll get you to the answer directly. |