According to the U.S. Department of Labor, the average American household spends

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 $259 and $1,019.

(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 $890 per year on household supplies?
(d) What proportion of households spend more than $1,280 per year on household supplies?
(e) What proportion of households spend between $350 and $490 on household supplies?

Explanation / Answer

UNIFORM DISTRIBUTION
PDF of uniform distribution f(x) = 1 / ( b - a ) for a < x < b
b = maximum Value
a = minimum Value
f(x) = 1/(b-a) = 1 / (1019-259) = 1 / 760 = 0.0013
a.
standard deviation = sqrt ( ( b - a ) ^ 2 / 12 )
=sqrt(1019-259)^2 / 12
=219.393
b.
mean = a + b / 2
=(259+1019)/2
=639
c.
P(X > 890) = (1019-890) * f(x)
= 129*0.0013
= 0.168 = 16.8%

d.

which is not possible to figured out, as maximum value of the distribution is 1019

e.
To find P(a < X < b) =( b - a ) * f(x)
P(350 < X < 490) = (490-350) * f(x)
= 140*0.0013
= 0.182 = 18.2%

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