Question

1. If x is a binomial random variable where n = 100 and p = 0.3,...

1. If x is a binomial random variable where n = 100 and p = 0.3, find the probability that x is less than or equal to 20 using the normal approximation to the binomial. Show work and excel functions if possible.

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Answer #1

If X ~ binomial (n,p) where n > 20 and 0.05 < p < 0.95 then approximately X has the Normal distribution with mean E(X) = np and standard deviation  

so is approximately N(0,1).

In this context, we have

n= 100

p = 0.3

E(X) = n*p = 100*0.3 = 30

The probability that x is less than or equal to 20 using the normal approximation to the binomial.

  

So, the probability that x is less than or equal to 20 is 0.0146

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