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December 10th, 2016, 01:28 PM   #1
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Cumulative distribution function

Hi people I have to answer the following question and I have´nt done that for a while.
"Fifty-five 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
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December 10th, 2016, 02:12 PM   #2
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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).

$\displaystyle \sum_{k=68}^{82} \binom{150}{k}(.55)^k{.45}^{150-k}$

To get a decent estimate you may want to use a normal distribution as an approximation.
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