Easy STATISTICS Standard Deviation Question, That Has For Some Reason Left Me Stumped :) HELP!?

Hi, I have a question that I'm just a bit confused on. I don't have the formula, so I don't understand what they are doing. I do have the right answer though. If you could explain this, that would be great!!!





A study shows that 20% of all births take place by C-section each year.





IN a random sample of 1000 births, how many on average will take place by C-section?


Answer: 200 (I understand this :)





What is the standard deviation of the number of C-section births in a sample of 1000?


Answer: 12.6 (How do I find this?)





Use your answers parts a and b to form an interval, within two standard deviations, that contians the number of C-section births in a sample of 1000.


Answer: (175, 225) (How? I thought you would just take the standard deviation and add and subtract it to the average)





THANK YOU! :)

Easy STATISTICS Standard Deviation Question, That Has For Some Reason Left Me Stumped :) HELP!?
Your situation here is an example of a binomial distribution, if you hadn't realized this already. The number of C-sections is a binomial random variable X. The standard deviation = the square root of (np(1-p)). In this case, sample size n is 1000, and probability p is 0.2. Putting these into the equation gives you a standard deviation of 12.6491, which matches your answer. Adding and subtracting two of these std. devs from your mean of 200 will give you an interval of roughly (175, 225.) Hope this helped...