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Question

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 193 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 47 voted.

 

The probability that fewer than 47 of 193 eligible voters voted is

Answer 1

David, the normal approximation applies a mean μ and standard deviation σ to a binomial distribution (Which is based on sample size n and probability p). Basically the approximated mean would be np and the standard deviation would be sqrt(npq) where q is 1-p. Last but not least we are given the sample point x=47. So now we can calculate a z value:

(x-np)/√npq=(47-42.46)/5.75=.7896

 

Which when referred to a z table, equates to: .7852 which means everything from 0 to 47 on the distribution with mean 42.46 and standard deviation of 5.75 would be 78.52% of the distribution.

Hope that helps!