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

55

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: