Title: Stats question Post by: bevywevy on Aug 18, 2014 Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!
Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units? Title: Re: Stats question Post by: ochorios on Aug 18, 2014 m(3wks)= 50+45+65 = 165
V(3wks) = 100+ 25 + 225 = 350, sqrt(350) = 18.708 z = (180-165)/18.7 = 15/18.7 = .8021 P(z > .8021) = 21.12% Title: Re: Stats question Post by: vanbu on Aug 18, 2014 Let X: demand for 3 weeks
E(X) = mean of X= 45+50+65 =160 Var(X) = ( 102+52+152) = 350 Stdev(X) = √350 = 18.708 X is normally distributed with ( 160,350) Now we want P( X >180) = P( (180-160)/18.7087) = P( z >1.069) =0.14253 There is a 14.253% chance that company will run out of units Title: Re: Stats question Post by: bevywevy on Aug 18, 2014 Thank you for your help! :)
Title: Re: Stats question Post by: ThePsychic on Aug 18, 2014 Who gets best answer?
Title: Re: Stats question Post by: bevywevy on Aug 18, 2014 I appreciate both of you helping, but Vanbu's answer I went with because he/she had 45+50+65 =160 where the other had these numbers equaling 165. An honest mistake; but I still went with Vanbu. Thanks again! ;D
Title: Re: Stats question Post by: MISSYH on Aug 19, 2014 So who is really right?
Title: Re: Stats question Post by: ThePsychic on Aug 19, 2014 Go with Vanbu's.
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