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?

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Business

Elaine Glass

12 March, 00:42

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?

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Alexzander Combs · Answer 1

a. 222.8

b. 0.002591

c. 0.2785

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

e. 0.142487

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