For this problem, you will be creating a probability distribution. Feel free to

Question

For this problem, you will be creating a probability distribution. Feel free to use StatCrunch. Then make your table in Word or Excel or even in StatCrunch if you prefer. You will be attaching a file to this problem as your response. It can be a picture like a JPG file, or a DOC file or XLS file of PDF file. In the city of Knoxville, 28.9% of the adult citizens smoke cigarettes. If 6 citizens are selected at random, let X be the random variable that counts how many of them smoke cigarettes. Create the probability distribution for X.

Explanation / Answer

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 6 * 0.289
= 1.734
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 6 * 0.289 * 0.711
= 1.23287
III.
standard deviation = sqrt( variance ) = sqrt(1.23287
=1.11035
when x =0,
P( X = 0 ) = ( 6 0 ) * ( 0.289^0) * ( 1 - 0.289 )^6
= 0.12919
P( X = 1 ) = ( 6 1 ) * ( 0.289^1) * ( 1 - 0.289 )^5
= 0.31506
P( X = 2 ) = ( 6 2 ) * ( 0.289^2) * ( 1 - 0.289 )^4
= 0.32016
P( X = 3 ) = ( 6 3 ) * ( 0.289^3) * ( 1 - 0.289 )^3
= 0.17351
P( X = 4 ) = ( 6 4 ) * ( 0.289^4) * ( 1 - 0.289 )^2
= 0.0529
P( X = 5 ) = ( 6 5 ) * ( 0.289^5) * ( 1 - 0.289 )^1
= 0.0086
P( X = 6 ) = ( 6 6 ) * ( 0.289^6) * ( 1 - 0.289 )^0
= 0.00058

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