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:

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.

d. Let Y be the number of gallons ordered. Find the probability mass function of Y.

e. Find the mean number of gallons ordered.

f. Find the variance of the number of gallons ordered.

g. Find the standard deviation of the number of gallons ordered.

Step 1 of 4:

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

We have to find

The mean number of drums ordered. The variance of the number drums ordered.The standard deviation of the number of drums ordered.Let Y be the number gallons ordered, then the probability mass function of Y.The mean number of gallons ordered.The variance of the number of drums ordered.The standard deviation of the number of gallons ordered.Step 2 of 4:

Since X is the number of drums ordered. The mean number of drums ordered.E(X) = P(x)

= (1+ (20.2) + (30.2) +( 40.1) +( 50.1)

= 2.3

Therefore the mean number of drums ordered = 2.3

(b) The variance of the drums ordered.

V(x) = E(X

E( ) =

= (

= 0.4 + 0.8 + 1.8+1.6+ 2.5

= 7.1

V(X) = 7.1 - 2.

= 1.81.

So the variance of the number of drums orders = 1.81.

(c) The standard deviation of the number of drums ordered

=

= 1.345

Therefore the standard deviation of the number of drums ordered is 1.345 .