### CFA Practice Question

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### CFA Practice Question

Given that X is a binomial random variable, with N = 5 and p = 0.3 and that we want to find P(X < 3), which of the following is true?

A. We can approximate P(XB < 3) with P(XN < 2.5).
B. We can approximate P(X < 3) using a normal with mean = 1.5 and standard deviation = 1.02.
C. We cannot approximate this binomial distribution with a normal distribution.

To approximate the binomial with a normal distribution, Np and N(1 - p) must both be greater than 5. Here, Np = (5)(0.3) = 1.5, which is not greater than 5. So, we cannot approximate P(X < 3) using a normal distribution [we would use a binomial table to find P(X < 3)].

User Comment
yanpz Why "to approximate the binomial with a normal distribution, Np and N(1-p) must both be greater than 5"?
whiteknight Also...why should we try to approximate the binomial with a normal distribution ?
bahodir Since NP and N(1-P) are greater than 5 means that N is a big number, we can somehow assume that the error from sampling is insignificant. Doing so, the shape of the your distribution may be similar to normal distribution
bahodir You may ask "why 5?"
It is a kind of convention, I guess.
StanleyMo Please refer here for more details:

http://en.wikipedia.org/wiki/Binomial_distribution
pranit Thank you StanleyMo. That was of great help.
johntan1979 Only if N > 30, then normal distribution.

Not sure where the Np and N(1-p) >5 comes from.