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June 8th, 2016, 08:11 AM  #1 
Newbie Joined: Jun 2016 From: Toronto, ON Posts: 5 Thanks: 0  Need help with this question
According to the National Work Intensification Survey, 42% of Americans felt their workload last year had significant more responsibility when compared to the start of the recession in December 2007. A random sample of five working Americans was selected. What is the probability that more than three of them felt their workload in 2011 had significant more responsibility when compared to the start of the recession in December 2007. I am unsure how to answer this. 
June 8th, 2016, 08:52 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
0.42 is a sample proportion, so it's a good estimator for the population proportion, which can also act as a probability in the context of this question. Basically, if X is the number of sampled Americans who felt their workload has increased significantly, than $\displaystyle X \sim Bin(n = 5, p = 0.47)$ and you have to find $\displaystyle P(X = 3, 4, 5)$ by adding up the binomial probabilities.

June 8th, 2016, 08:58 AM  #3 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
By Bernoulli trial: $\displaystyle P(4)=\binom{5}{4}\cdot 0.42^4\cdot (10.42)^{54}$ $\displaystyle P(5)=\binom{5}{5}\cdot 0.42^5\cdot (10.42)^{55}$ $\displaystyle P(>3)=P(4)+P(5)$ 
June 8th, 2016, 09:27 AM  #4 
Newbie Joined: Jun 2016 From: Toronto, ON Posts: 5 Thanks: 0 
Where do you take it from there?

June 8th, 2016, 12:30 PM  #5 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77  

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