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 $251 and $1,027.
(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 $870 per year on household supplies?
(d) What proportion of households spend more than $1,290 per year on household supplies?
(e) What proportion of households spend between $380 and $490 on household supplies?

a)

And the deviation would be:

b)

c)

d)

e)

Step-by-step explanation:

For this case we define the random variable X as "American household spend" and we know that the distribution for X is given by:

Part a

We can calculate the variance first with this formula:

And the deviation would be:

Part b

For this case the height represent the individual probability for any value in the interval and is given by:

Part c

For this case we can use the cumulative distribution function given by:

We want this probability:

Part d

For this case we can use the cumulative distribution function given by:

We want this probability:

Part e

We want this probability: