A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $225,000. a. If she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price? b. If she leaves it on the market for another month, what is the probability she will get at least $215,000 for the house? c. If she leaves it on the market for another month, what is the probability she will get less than $210,000? d. Should the executive leave the house on the market for another month? Why or why not?

Question

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Answer 1

Textbook Question

Chapter 6, Problem 33SE

A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $225,000.

a. If she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price?
b. If she leaves it on the market for another month, what is the probability she will get at least $215,000 for the house?
c. If she leaves it on the market for another month, what is the probability she will get less than $210,000?
d. Should the executive leave the house on the market for another month? Why or why not?

a.

Expert Solution

To determine

Obtain the mathematical expression for the probability density function.

Answer to Problem 33SE

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Explanation of Solution

Calculation:

The executive’s employer offers to buy a house for $210,000 and this offer will be expired by the end of the week. Post discussion with business executive’s relator, the seller believes that by leaving the house in the market for another month, the price for house will be uniformly distributed between $200,000 and $225,000.

The probability density function for uniform distribution is,

f(x)={1b−a for a≤x≤b0 elsewhere.

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

b.

Expert Solution

To determine

Find the probability that the house will get with at least $215,000.

Answer to Problem 33SE

The probability that the house will get with at least $215,000 is 0.4.

Explanation of Solution

Calculation:

The cumulative density function for uniform distribution is,

P(x≤X)=X−ab−a

The probability that the house will get with at least $215,000 is,

P(x>215,000)=1−P(x≤215,000)=1−215,000−200,00025,000=1−15,00025,000=0.4

Thus, the value ofP(x>215,000)is 0.4.

c.

Expert Solution

To determine

Find the probability that the house will get less than $210,000.

Answer to Problem 33SE

The probability that the house will get less than $210,000 is 0.4.

Explanation of Solution

Calculation:

The probability that the house will get less than $210,000 is,

P(x<210,000)=210,000−200,00025,000=10,00025,000=0.4

Thus, the value ofP(x<210,000)is 0.4.

d.

Expert Solution

To determine

Explain whether the executive can leave the house in the market for another month or not.

Explanation of Solution

Calculation:

If the house is left in market for another month, the average sales price of house is,

E(x)=a+b2=200,000+225,0002=425,0002=212,500

This indicates that if the executive leaves the house in the market for another month, then the expected sales price is $2,500 higher than the before price $210,000. If the house is left in the market for another month, the executive will get less than the company’s offer with 0.4 probability. It represents that it is better for the executive to leave the house for another month in the market with an expected cost of $215,000.

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Answer 2

Textbook Question

Chapter 6, Problem 33SE

A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $225,000.

a. If she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price?
b. If she leaves it on the market for another month, what is the probability she will get at least $215,000 for the house?
c. If she leaves it on the market for another month, what is the probability she will get less than $210,000?
d. Should the executive leave the house on the market for another month? Why or why not?

a.

Expert Solution

To determine

Obtain the mathematical expression for the probability density function.

Answer to Problem 33SE

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Explanation of Solution

Calculation:

The executive’s employer offers to buy a house for $210,000 and this offer will be expired by the end of the week. Post discussion with business executive’s relator, the seller believes that by leaving the house in the market for another month, the price for house will be uniformly distributed between $200,000 and $225,000.

The probability density function for uniform distribution is,

f(x)={1b−a for a≤x≤b0 elsewhere.

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

b.

Expert Solution

To determine

Find the probability that the house will get with at least $215,000.

Answer to Problem 33SE

The probability that the house will get with at least $215,000 is 0.4.

Explanation of Solution

Calculation:

The cumulative density function for uniform distribution is,

P(x≤X)=X−ab−a

The probability that the house will get with at least $215,000 is,

P(x>215,000)=1−P(x≤215,000)=1−215,000−200,00025,000=1−15,00025,000=0.4

Thus, the value ofP(x>215,000)is 0.4.

c.

Expert Solution

To determine

Find the probability that the house will get less than $210,000.

Answer to Problem 33SE

The probability that the house will get less than $210,000 is 0.4.

Explanation of Solution

Calculation:

The probability that the house will get less than $210,000 is,

P(x<210,000)=210,000−200,00025,000=10,00025,000=0.4

Thus, the value ofP(x<210,000)is 0.4.

d.

Expert Solution

To determine

Explain whether the executive can leave the house in the market for another month or not.

Explanation of Solution

Calculation:

If the house is left in market for another month, the average sales price of house is,

E(x)=a+b2=200,000+225,0002=425,0002=212,500

This indicates that if the executive leaves the house in the market for another month, then the expected sales price is $2,500 higher than the before price $210,000. If the house is left in the market for another month, the executive will get less than the company’s offer with 0.4 probability. It represents that it is better for the executive to leave the house for another month in the market with an expected cost of $215,000.

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Answer 3

Textbook Question

Chapter 6, Problem 33SE

A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $225,000.

a. If she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price?
b. If she leaves it on the market for another month, what is the probability she will get at least $215,000 for the house?
c. If she leaves it on the market for another month, what is the probability she will get less than $210,000?
d. Should the executive leave the house on the market for another month? Why or why not?

a.

Expert Solution

To determine

Obtain the mathematical expression for the probability density function.

Answer to Problem 33SE

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Explanation of Solution

Calculation:

The executive’s employer offers to buy a house for $210,000 and this offer will be expired by the end of the week. Post discussion with business executive’s relator, the seller believes that by leaving the house in the market for another month, the price for house will be uniformly distributed between $200,000 and $225,000.

The probability density function for uniform distribution is,

f(x)={1b−a for a≤x≤b0 elsewhere.

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

b.

Expert Solution

To determine

Find the probability that the house will get with at least $215,000.

Answer to Problem 33SE

The probability that the house will get with at least $215,000 is 0.4.

Explanation of Solution

Calculation:

The cumulative density function for uniform distribution is,

P(x≤X)=X−ab−a

The probability that the house will get with at least $215,000 is,

P(x>215,000)=1−P(x≤215,000)=1−215,000−200,00025,000=1−15,00025,000=0.4

Thus, the value ofP(x>215,000)is 0.4.

c.

Expert Solution

To determine

Find the probability that the house will get less than $210,000.

Answer to Problem 33SE

The probability that the house will get less than $210,000 is 0.4.

Explanation of Solution

Calculation:

The probability that the house will get less than $210,000 is,

P(x<210,000)=210,000−200,00025,000=10,00025,000=0.4

Thus, the value ofP(x<210,000)is 0.4.

d.

Expert Solution

To determine

Explain whether the executive can leave the house in the market for another month or not.

Explanation of Solution

Calculation:

If the house is left in market for another month, the average sales price of house is,

E(x)=a+b2=200,000+225,0002=425,0002=212,500

This indicates that if the executive leaves the house in the market for another month, then the expected sales price is $2,500 higher than the before price $210,000. If the house is left in the market for another month, the executive will get less than the company’s offer with 0.4 probability. It represents that it is better for the executive to leave the house for another month in the market with an expected cost of $215,000.

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Answer 4

Textbook Question

Chapter 6, Problem 33SE

A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $200,000 and $225,000.

a. If she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price?
b. If she leaves it on the market for another month, what is the probability she will get at least $215,000 for the house?
c. If she leaves it on the market for another month, what is the probability she will get less than $210,000?
d. Should the executive leave the house on the market for another month? Why or why not?

a.

Expert Solution

To determine

Obtain the mathematical expression for the probability density function.

Answer to Problem 33SE

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Explanation of Solution

Calculation:

The executive’s employer offers to buy a house for $210,000 and this offer will be expired by the end of the week. Post discussion with business executive’s relator, the seller believes that by leaving the house in the market for another month, the price for house will be uniformly distributed between $200,000 and $225,000.

The probability density function for uniform distribution is,

f(x)={1b−a for a≤x≤b0 elsewhere.

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

b.

Expert Solution

To determine

Find the probability that the house will get with at least $215,000.

Answer to Problem 33SE

The probability that the house will get with at least $215,000 is 0.4.

Explanation of Solution

Calculation:

The cumulative density function for uniform distribution is,

P(x≤X)=X−ab−a

The probability that the house will get with at least $215,000 is,

P(x>215,000)=1−P(x≤215,000)=1−215,000−200,00025,000=1−15,00025,000=0.4

Thus, the value ofP(x>215,000)is 0.4.

c.

Expert Solution

To determine

Find the probability that the house will get less than $210,000.

Answer to Problem 33SE

The probability that the house will get less than $210,000 is 0.4.

Explanation of Solution

Calculation:

The probability that the house will get less than $210,000 is,

P(x<210,000)=210,000−200,00025,000=10,00025,000=0.4

Thus, the value ofP(x<210,000)is 0.4.

d.

Expert Solution

To determine

Explain whether the executive can leave the house in the market for another month or not.

Explanation of Solution

Calculation:

If the house is left in market for another month, the average sales price of house is,

E(x)=a+b2=200,000+225,0002=425,0002=212,500

This indicates that if the executive leaves the house in the market for another month, then the expected sales price is $2,500 higher than the before price $210,000. If the house is left in the market for another month, the executive will get less than the company’s offer with 0.4 probability. It represents that it is better for the executive to leave the house for another month in the market with an expected cost of $215,000.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Obtain the mathematical expression for the probability density function.

Answer to Problem 33SE

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Explanation of Solution

Calculation:

The executive’s employer offers to buy a house for $210,000 and this offer will be expired by the end of the week. Post discussion with business executive’s relator, the seller believes that by leaving the house in the market for another month, the price for house will be uniformly distributed between $200,000 and $225,000.

The probability density function for uniform distribution is,

f(x)={1b−a for a≤x≤b0 elsewhere.

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

b.

Expert Solution

To determine

Find the probability that the house will get with at least $215,000.

Answer to Problem 33SE

The probability that the house will get with at least $215,000 is 0.4.

Explanation of Solution

Calculation:

The cumulative density function for uniform distribution is,

P(x≤X)=X−ab−a

The probability that the house will get with at least $215,000 is,

P(x>215,000)=1−P(x≤215,000)=1−215,000−200,00025,000=1−15,00025,000=0.4

Thus, the value ofP(x>215,000)is 0.4.

c.

Expert Solution

To determine

Find the probability that the house will get less than $210,000.

Answer to Problem 33SE

The probability that the house will get less than $210,000 is 0.4.

Explanation of Solution

Calculation:

The probability that the house will get less than $210,000 is,

P(x<210,000)=210,000−200,00025,000=10,00025,000=0.4

Thus, the value ofP(x<210,000)is 0.4.

d.

Expert Solution

To determine

Explain whether the executive can leave the house in the market for another month or not.

Explanation of Solution

Calculation:

If the house is left in market for another month, the average sales price of house is,

E(x)=a+b2=200,000+225,0002=425,0002=212,500

This indicates that if the executive leaves the house in the market for another month, then the expected sales price is $2,500 higher than the before price $210,000. If the house is left in the market for another month, the executive will get less than the company’s offer with 0.4 probability. It represents that it is better for the executive to leave the house for another month in the market with an expected cost of $215,000.

Answer 8

a.

Expert Solution

To determine

Obtain the mathematical expression for the probability density function.

Answer to Problem 33SE

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Explanation of Solution

Calculation:

The executive’s employer offers to buy a house for $210,000 and this offer will be expired by the end of the week. Post discussion with business executive’s relator, the seller believes that by leaving the house in the market for another month, the price for house will be uniformly distributed between $200,000 and $225,000.

The probability density function for uniform distribution is,

f(x)={1b−a for a≤x≤b0 elsewhere.

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Obtain the mathematical expression for the probability density function.

Answer 13

Answer to Problem 33SE

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Answer 14

Explanation of Solution

Calculation:

The executive’s employer offers to buy a house for $210,000 and this offer will be expired by the end of the week. Post discussion with business executive’s relator, the seller believes that by leaving the house in the market for another month, the price for house will be uniformly distributed between $200,000 and $225,000.

The probability density function for uniform distribution is,

f(x)={1b−a for a≤x≤b0 elsewhere.

The probability density function for sales price is,

f(x)={125,000 for 200,000≤x≤250,0000 elsewhere.

Answer 15

b.

Expert Solution

To determine

Find the probability that the house will get with at least $215,000.

Answer to Problem 33SE

The probability that the house will get with at least $215,000 is 0.4.

Explanation of Solution

Calculation:

The cumulative density function for uniform distribution is,

P(x≤X)=X−ab−a

The probability that the house will get with at least $215,000 is,

P(x>215,000)=1−P(x≤215,000)=1−215,000−200,00025,000=1−15,00025,000=0.4

Thus, the value ofP(x>215,000)is 0.4.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Find the probability that the house will get with at least $215,000.

Answer 20

Answer to Problem 33SE

The probability that the house will get with at least $215,000 is 0.4.

Answer 21

Explanation of Solution

Calculation:

The cumulative density function for uniform distribution is,

P(x≤X)=X−ab−a

The probability that the house will get with at least $215,000 is,

P(x>215,000)=1−P(x≤215,000)=1−215,000−200,00025,000=1−15,00025,000=0.4

Thus, the value ofP(x>215,000)is 0.4.

Answer 22

c.

Expert Solution

To determine

Find the probability that the house will get less than $210,000.

Answer to Problem 33SE

The probability that the house will get less than $210,000 is 0.4.

Explanation of Solution

Calculation:

The probability that the house will get less than $210,000 is,

P(x<210,000)=210,000−200,00025,000=10,00025,000=0.4

Thus, the value ofP(x<210,000)is 0.4.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Find the probability that the house will get less than $210,000.

Answer 27

Answer to Problem 33SE

The probability that the house will get less than $210,000 is 0.4.

Answer 28

Explanation of Solution

Calculation:

The probability that the house will get less than $210,000 is,

P(x<210,000)=210,000−200,00025,000=10,00025,000=0.4

Thus, the value ofP(x<210,000)is 0.4.

Answer 29

d.

Expert Solution

To determine

Explain whether the executive can leave the house in the market for another month or not.

Explanation of Solution

Calculation:

If the house is left in market for another month, the average sales price of house is,

E(x)=a+b2=200,000+225,0002=425,0002=212,500

This indicates that if the executive leaves the house in the market for another month, then the expected sales price is $2,500 higher than the before price $210,000. If the house is left in the market for another month, the executive will get less than the company’s offer with 0.4 probability. It represents that it is better for the executive to leave the house for another month in the market with an expected cost of $215,000.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

Explain whether the executive can leave the house in the market for another month or not.

Answer 34

Explanation of Solution

Calculation:

If the house is left in market for another month, the average sales price of house is,

E(x)=a+b2=200,000+225,0002=425,0002=212,500

This indicates that if the executive leaves the house in the market for another month, then the expected sales price is $2,500 higher than the before price $210,000. If the house is left in the market for another month, the executive will get less than the company’s offer with 0.4 probability. It represents that it is better for the executive to leave the house for another month in the market with an expected cost of $215,000.