
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 6,759 Thanks: 696  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: 6,759 Thanks: 696  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: 6,759 Thanks: 696  Re: approximation problem Quote:
 

Tags 
approximation, problem 
Search tags for this page 
approximate median age of residents,the median age of residents of the united states is 31 years. if a survey of 100 randomly selected united states residents is taken, find the approximate probability,what is the approximate of 59.5
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
approximation problem  lovelypippy  Elementary Math  1  December 20th, 2013 04:35 PM 
Linear approximation problem  84grandmarquis  Applied Math  2  October 20th, 2013 04:50 PM 
Approximation Problem  mathkid  Calculus  4  November 18th, 2012 08:33 PM 
need help with linear approximation problem  pdeep  Calculus  4  November 2nd, 2011 03:11 AM 
Derivatives/linear approximation problem  TsAmE  Calculus  1  April 26th, 2010 03:33 PM 