SOLUTION: The mean and standard deviation of the binomial distribution are 4 and 1.633 respectively. Find n,p and the distribution function at X=3.

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Question 1161376: The mean and standard deviation of the binomial distribution are 4 and 1.633 respectively. Find n,p and the distribution function at X=3.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
The mean and standard deviation of the binomial distribution are 4 and 1.633
respectively. Find n,p and the distribution function at X=3.
system%28mu=4=np%2Csigma=1.633=sqrt%28np%281-p%29%29%29

Substitute 4 for np in the second equation

1.633=sqrt%28%281-p%29%29 

Square both sides

1.633%5E2=%28sqrt%284%281-p%29%29%29%5E2

2.666689=4%281-p%29

Distribute:

2.666689=4-4p

Add -4 to both sides

-1.333311=-4p

Divide both sides by -4

0.33332775=p

Substitute in

4=np

4=n%280.33332775%29

Divide both sides by 0.33332775

12.000201=n

I'd round off to p = 0.3333 and n = 12

On your TI-84

press 2nd vars and scroll to A:binompdf(

make it read this

trials:12
p:3333
x value:3
Paste

Scroll down to "Paste"
Press enter

read

binompdf(12,0.3333,3)

Press enter

0.2119838219    <--answer

Edwin