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December 10th, 2016, 12:28 PM  #1 
Newbie Joined: Dec 2016 From: Trinidad and Tobago Posts: 5 Thanks: 0  Cumulative distribution function
Hi people I have to answer the following question and I have´nt done that for a while. "Fiftyfive percent of all students on a campus are in Humanities. If 150 students are selected at random, what is the probability that the proportion of Humanities students in this particular sample will be between 45% and 55%." I thought I could solve itwith the cummulative mass function, therefore I would have to calculate F(0.55) and F (0.45) First I tried to Calculate F(0.55) while I did the following: (150!/(82.5!*67.5!)*0.55^82.5*0.45^67.5=0.065 which would mean that the probability for havving less of equal to 55% would only be 6.5% which seems to be to small. Can anyone help me detecting the error? Bes Jens 
December 10th, 2016, 01:12 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,276 Thanks: 516 
Your model is wrong. You are calculating the probability that exactly 82.5 students are in the humanities. A more precise estimate (assuming the number of students is an integer). $\displaystyle \sum_{k=68}^{82} \binom{150}{k}(.55)^k{.45}^{150k}$ To get a decent estimate you may want to use a normal distribution as an approximation. 

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