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.

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