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According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 people in Uganda. Let X = the number of people who have access to electricity.Using the formulas, calculate the mean and standard deviation of X.

 Feb 26, 2019
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In this case, we are given sample size n and probability p so this is a binomial distribution.

 

We can use the normal approximation where the mean is np and the standard deviation is the square root of npq where q=1-p. Then mean is 150*.09=13.5 and the standard deviation is the square root of 12.285 or 3.5.

 

I used Excel here but basically, I calculated the binomial probability with n=150, p=.09, and x=15 to be: .099

 

The cumulative binomial probability with n=150, p=.09, and x=10 is .1987

 

The cumulative binomial probability of having at most 25 people have electricity (n=150,p=.09, x=25) is 99.9%. So the probability of having more than 25 people is 1-.999=.0001.

 

Hope that helps!  cool

 Feb 26, 2019

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