CFA Practice Question

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CFA Practice Question

For X, a binomial random variable with N = 70 and p = 0.3, we can approximate P(X < 19) by using a normal distribution with ______.

A. mean 70 and standard deviation 0.3
B. mean 21 and standard deviation 3.83
C. mean 70 and standard deviation 3.83
Correct Answer: B

We can approximate the binomial with a normal distribution because Np = 21 is greater than 5 and N(1 - P) = 49 is greater than 5. The normal distribution that we use to do the approximation has mean = Np = 21 and a standard deviation square root of N(p)(1 - p), in this case, 3.83 (to the nearest 0.01).

User Contributed Comments 9

User Comment
mtcfa What the heck does "5" have to do with anything???
grantw The common rule is that you can approximate the binomial with the normal when np and n(1-p) both exceed some magic number. That magic number is variously stated as 5, 10 or 15, depending on the conservative nature of the statistician, the higher the magic number, the more conservative the statistician.

TammTamm mtcfa, those are my same sentiments. LOL I hate Quant Methods, this is a bunch of bunk if you ask me. Anywho, that's my .02cents.
magicchip Captain Kirk said "Make it so.."
rsanfo Actually, Captain Picard said "Make it so...". Captain Kirk said "How many women on this planet do I get to kiss?".
poomie83 Does anyone know the magic number the cfa wants us to use?
fanDango 42
FozzeyBear this some stupid stuff
ashish100 It's complex.

42 explains it perfectly tho.
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