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January 24th, 2012, 06:44 PM  #1 
Senior Member Joined: Nov 2009 Posts: 169 Thanks: 0  approximation problem
The median age of residents of the United States is 31 years. If a survey of 100 randomly selected U.S. residents is to be taken, what is the approximate probability that at least 60 will be under 31 years of age? it seems like a normal approximate binomial question, but I don't know what median age mean, is it just the mean of the ages, or the median of the age, how do I use the approximation if I only kow the median of it? 
January 25th, 2012, 03:19 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 723  Re: approximation problem
Median means half of the population is greater and half less. To calculate what you want exactly you need to use binomial distribution, summing from 60 to 100, where the total is 100. Alternatively you can use an approximate normal with mean = 50 and standard deviation = 5. The probability then is the probability of more than 2 standard deviations on one side. 
January 25th, 2012, 07:32 PM  #3 
Senior Member Joined: Nov 2009 Posts: 169 Thanks: 0  Re: approximation problem
so I used normal N~(50,5) p(y>=60)=p(y>=59.5)=p(z>=59.550/5)=p(z>=1.9)=0.0287 which does not make sense since as p=0.5, p(y>=60) should be something around 0.4, the probability I got is too small, anyone know why?

January 25th, 2012, 09:43 PM  #4  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: approximation problem Quote:
 
January 26th, 2012, 12:20 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 723  Re: approximation problem
Using the notation already used, the probability you want is P(z>2). I presume that is how Erimess got his answer.

January 26th, 2012, 06:46 PM  #6 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: approximation problem
Well, that's how Erimess got the answer she used. 
January 27th, 2012, 01:29 PM  #7  
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 723  Re: approximation problem Quote:
 

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