Question

According to the U.S. Department of Labor, the average American household spends $639 on household supplies per year. Suppose annual expenditures on household supplies per household are uniformly distributed between the values of $261 and $1,017. (a) What is the standard deviation of this distribution? (b) What is the height of this distribution? (c) What proportion of households spend more than $900 per year on household supplies? (d) What proportion of households spend more than $1,220 per year on household supplies? (e) What proportion of households spend between $330 and $510 on household supplies?

Answer 1

a. 222.8

b. 0.002591

c. 0.2785

d. P(X>1290) =0 as 1290 lies outside.

e. 0.142487

Step-by-step explanation:

a) std deviation =(b-a)/(12)1/2 =(1025-253)/(12)1/2 =222.8572

b) as area =1

(1/2)*height*(1025-253)=1

height of this distribution =2/(1025-253)=0.002591

c) P(X>810)=(1025-810)/(1025-253)=0.2785

d)P(X>1290) =0 as 1290 lies outside.

e)P(370<x<480)= (480-370)/(1025-253)=0.142487