
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 10th, 2016, 01:28 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, 02:12 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,216 Thanks: 493 
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. 

Tags 
cumulative, distribution, function 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cumulative distribution function help! (CDF)  sharpknight  Advanced Statistics  0  September 18th, 2014 11:18 PM 
Cumulative distribution function proof  etham  Advanced Statistics  1  November 24th, 2013 02:10 PM 
Interpretation of N(.) cumulative distribution function  Aqil  Advanced Statistics  0  March 9th, 2013 11:13 AM 
Negative binomial cumulative distribution function  illusion419  Advanced Statistics  1  July 25th, 2011 06:40 PM 
cumulative distribution function question  sneaky  Algebra  1  October 8th, 2010 01:48 PM 