Expected Repairs for Leased Computer: Calculating Mean and Standard Deviation

[mutzy188]

Hi I need some help. I don't think I did any of this right.

A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company's research suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1% three times, and none required more than three repairs.

1. Find the expected number of repairs this kind of computer is expected to need each year.

100(.86) + 125(.09) + 150(.04) + 175(.01) = 105

2. Find the standard deviation of the number of repairs each year.

.86(100-105)^2 + .09(125-105)^2 + .04(150-105)^2 + .01(175-105)^2 = 187.5
sqrt(187.5) = 13.69

3. What are the mean and standard deviation of the company's annual expense for the service contract?
I have no clue how to do this one.

4. How many times should the company expect to have to get this computer repaired over the three-year term of lease?
None?

5. What is the standard deviation of the number of repairs that may be required during the three-year lease period?
105*3 = 315

Thanks

 

[Galileo]

Hi I need some help. I don't think I did any of this right.

A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company's research suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1% three times, and none required more than three repairs.

1. Find the expected number of repairs this kind of computer is expected to need each year.

100(.86) + 125(.09) + 150(.04) + 175(.01) = 105

An answer like 105 should tell you something is wrong.
Use the right information: A computer needs no repairs with a probability of 86%. 1 repair with a prob. of 9%, 2 repairs with 4% and three with 1%.
Find the expectation $P(X)$ from this.

1. Find the expectation of the number of repairs squared: $P(X^2)$.
Then use: $\sigma_X^2=P(X^2)-P(X)^2$

 

[xanthym]

Hi I need some help. I don't think I did any of this right.

A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company's research suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1% three times, and none required more than three repairs.

1. Find the expected number of repairs this kind of computer is expected to need each year.
100(.86) + 125(.09) + 150(.04) + 175(.01) = 105
E(X) = μ = (0.86)*(0) + (0.09)*(1) + (0.04)*(2) + (0.01)*(3) = 0.20

2. Find the standard deviation of the number of repairs each year.
.86(100-105)^2 + .09(125-105)^2 + .04(150-105)^2 + .01(175-105)^2 = 187.5
sqrt(187.5) = 13.69
{Variance of X} = σ^2 = E{X^2} - E^2{X}


3. What are the mean and standard deviation of the company's annual expense for the service contract?
I have no clue how to do this one.
{Mean of X} = E{X} = μ
{Variance of X} = E{X^2} - E^2{X} = σ^2
{Yearly Cost} = C = 100 + 25*X
E{C} = E{100 + 25*X} = E{100} + E{25*X} = 100 + 25*E{X} =
= 100 + 25*μ
E{C^2} - E^2{C} = {calculate & collect terms} = (25^2)*σ^2

4. How many times should the company expect to have to get this computer repaired over the three-year term of lease?
None?
{Mean of X} = E{X} = μ
E{X1 + X2 + X3} = E{X1} + E{X2} + E{X3} = 3*μ

5. What is the standard deviation of the number of repairs that may be required during the three-year lease period?
105*3 = 315
{Variance of X} = E{X^2} - E^2{X} = σ^2
{Variance of (X1 + X2 + X3)} =
= E{(X1 + X2 + X3)^2} - E^2{(X1 + X2 + X3)} =
= {calculate & collect terms} = 9*σ^2

Thanks

HINTS GIVEN ABOVE IN RED.
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