Need statistics help with twenty-eight percent of college students who use credit card

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twenty-eight percent of college students say they use credit card because of rewards program. you randomly select 10 college students and ask them to name the reason they use credit cards. find the probability that the number of college studuents who say they use credit cards because of the rewards program is exactly two or at least two

Dec 1st, 2015

Thank you for the opportunity to help you with your question!

You may solve this question either using Binomial Distribution or Poisson Distribution.

Let's use Poisson for easy calculation and it is defined as,

P(X=x) = {e^(-l) * (l^x)}/x!

Here l = np  where n= 10 and p=28% = 0.28

Hence l= 10* 0.28 = 2.8

They asked prob exactly equal to 2 

P(X=2) = {e^(-2.8) * (2.8^2)}/2! = 0.0608*3.92 = 0.2383

Also

P(atleast two) = 1-P(x<2) = 1-{P(X=0)+P(X=1)} = 1- e^-2.8{1+2.8} = 1- 0.2310 = 0.7689

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 1st, 2015

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