A chemical supply company ships a certain sol- vent in 10-gallon drums. Let X represent the num- ber of drums ordered by a randomly chosen cus- tomer. Assume X has the following probability mass function:x 0 1 2 3 4p(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.(d) Let Y be the number of gallons ordered. Find the probability mass function of Y(e) Find the mean number of gallons ordered.

a) 1.3

b) 1.81

c) 1.345

d) Each drum is a 10-gallon drum

In terms of gallons, the probability mass function becomes

y 0 10 20 30 40

p(y) 0.4 0.2 0.2 0.1 0.1

e) 13 gallons

Step-by-step explanation:

a) The mean is given by the expected value for number of drums ordered.

Expected values is given by

E(X) = Σ xᵢpᵢ

x 0 1 2 3 4

p(x) 0.4 0.2 0.2 0.1 0.1

E(X) = (0×0.4) + (1×0.2) + (2×0.2) + (3×0.1) + (4×0.1) = 0 + 0.2 + 0.4 + 0.3 + 0.4 = 1.3

b) Variance = Var(X) = Σx²p − μ²

μ = E(X) = mean

Σx²p = (0² × 0.4) + (1² × 0.2) + (2² × 0.2) + (3² × 0.1) + (4² × 0.1) = 0 + 0.2 + 0.8 + 0.9 + 1.6 = 3.5

Var(X) = Σx²p − μ² = 3.5 - 1.3² = 1.81

c) Standard deviation = √variance = √1.81 = 1.345

d) Each drum is a 10-gallon drum

In terms of gallons, the probability mass function becomes

y 0 10 20 30 40

p(y) 0.4 0.2 0.2 0.1 0.1

e) Mean = E(Y)

E(Y) = Σ yᵢpᵢ

E(Y) = (0×0.4) + (10×0.2) + (20×0.2) + (30×0.1) + (40×0.1) = 13 gallons

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

answer: input the dimensions of the room to be painted. click the button to calculate the amount of paint and man-hours needed for this job.

interior paint coverage depends on the brand of paint used. the coverage amount is listed on the label of the paint can. use this to adjust the values in the paint coverage section below. paint usually is applied at 350 to 400 square feet per gallon (primer at 200 to 300 square feet per gallon).

step-by-step explanation: