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

the median here is 25. your lowest value is 14 and highest value is 48. to find the third quartile, find the medium number in between 25 and 48 which would be 42 i believe.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|