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31 August, 17:12

A chemical supply company ships a certain solvent in 10-gallon drums. Let X represent the number of drums ordered by a randomly chosen customer. Assume X has the following probability mass function:

x 0 1 2 3 4

p (x) 0.4 0.2 0.2 0.1 0.1

(a) Find the mean number of drums ordered.

(b) Find the variance of the number of drums ordered.

(c) Find the standard deviation of the number of drums ordered.

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  1. 31 August, 17:41
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    a) 1.3

    b) 1.81

    c) 1.345

    Step-by-step explanation:

    a)

    Mean number of drums = E (x) = sum[x*p (x) ]

    x p (x) x*p (x)

    0 0.4 0

    1 0.2 0.2

    2 0.2 0.4

    3 0.1 0.3

    4 0.1 0.4

    Mean number of drums=0+0.2+0.4+0.3+0.4

    Mean number of drums=1.3

    b)

    Variance of the number of drums = E (x²) - [E (x) ]² = sum[x²*p (x) ]-[sum[x*p (x) ]]²

    x p (x) x*p (x) x² x²*p (x)

    0 0.4 0 0 0

    1 0.2 0.2 1 0.2

    2 0.2 0.4 4 0.8

    3 0.1 0.3 9 0.9

    4 0.1 0.4 16 1.6

    E (x²) = sum[x²*p (x) ]=0+0.2+0.8+0.9+1.6=3.5

    Variance of the number of drums=3.5-[1.3]²

    Variance of the number of drums=3.5-1.69

    Variance of the number of drums=1.81

    c)

    Standard deviation of the number of drums=√Variance of the number of drums

    Standard deviation of the number of drums=√1.81

    Standard deviation of the number of drums=1.345
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