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 $263 and $1,015.

(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 $880 per year on household supplies? (d) What proportion of households spend more than $1,260 per year on household supplies? (e) What proportion of households spend between $370 and $500 on household supplies?

(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 $830 per year on household supplies? (d) What proportion of households spend more than $1,250 per year on household supplies? (e) What proportion of households spend between $340 and $500 on household supplies?

Answer 1

ANSWER:

1a)

pdf of Uniform Distribution is given by:

                               a < x < b

Here,

a = 263

b = 1015.

So, we get:

            = 1/752 = 0.0013

                                263 < x< 1015.

(a) SD of Uniform Distribution is given by:

Substituting the values of a anb, we get:

(b) The height of this distribution is given by: 0.0013

(

ANOTHER ANSWER..... 2a)

pdf of Uniform Distribution is given by:

                               a < x < b

Here,

a = 263

b = 1015.

So, we get:

            = 1/752 = 0.0013

                                263 < x< 1015.

(a) SD of Uniform Distribution is given by:

Substituting the values of a anb, we get

(b) The height of this distribution is given by: 0.0013

(c) P(X > 830):

(d) P(X > 1250) = 0

REASON: Value upto only 1015 is there.

(e) P(340 < X < 500):

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