Question

In: Math

Each​ year, ratings are compiled concerning the performance of new cars during the first 60 days...

Each​ year, ratings are compiled concerning the performance of new cars during the first 60 days of use. Suppose that the cars have been categorized according to whether a car needs​ warranty-related repair​ (yes or​ no) and the country in which the company manufacturing a car is based​ (in some country X or not in country​ X). Based on the data​ collected, the probability that the new car needs a warranty repair is 0.07​, the probability that the car is manufactured by a company based in country X is 0.50, and the probability that the new car needs a warranty repair and was manufactured by a company based in country X is 0.025. Use this information to answer​ (a) through​ (d) below.

a.Suppose you know that a company based in country X manufactured a particular car. What is the probability that the car needs warranty​ repair?

​(Round to three decimal places as​ needed.)

b. Suppose you know that a company based in country X did not manufacture a particular car. What is the probability that the car needs warranty​ repair?

​(Round to three decimal places as​ needed.)

c. Are need for warranty repair and location of the company manufacturing the car​ independent?

A.

No

B.

Yes

C.

Not enough information

Solutions

Expert Solution

Given:

P(Repair) = 0.07

P(Repair AND based on country X) = 0.025

P(Company based in country X) = 0.50

P(Company did not base in country X) = 1 - 0.50 = 0.50

(a) P(Warranty repair| based in country X) that is a conditional probability.

The formula to find the conditional probability is,

The probability that the car needs warranty​ repair given that based in country X is 0.05

(b) P(Repair| did not based in country X) that is a conditional probability.

Using the total law of probability, we can write P(Repair) as,

P(Repair) = P(Repair AND based on country X) + P(Repair AND did not base on country X)

0.07 = 0.025 + P(Repair AND did not base on country X)

P(Repair AND did not base on country X) = 0.07 - 0.025 = 0.045

The formula of conditional probability is,

The probability that the car needs warranty​ repair given that did not base on country X is 0.09

(c) Two events are independent when P(A AND B) = P(A) * P(B)

Here A: Repair and B: base on country X

P(Repair AND based on country X) = 0.025

P(Repair) * P(based on country X) = 0.07 * 0.50 = 0.035

That is P(A AND B) not equal to P(A) * P(B)

Therefore, need for warranty repair and location of the company manufacturing the car​ are not independent.

The answer is No.

milcah answered 1 year ago
Next > < Previous

Related Solutions

Each​ year, ratings are compiled concerning the performance of new cars during the first 30 days...
Each​ year, ratings are compiled concerning the performance of new cars during the first 30 days of use. Suppose that the cars have been categorized according to whether a car needs​ warranty-related repair​ (yes or​ no) and the country in which the company manufacturing a car is based​ (in some country X or not in country​ X). Based on the data​ collected, the probability that the new car needs a warranty repair is 0.08, the  probability that the car is manufactured...
Each year, ratings are compiled concerning the performance of new cars during the firs 90 days...
Each year, ratings are compiled concerning the performance of new cars during the firs 90 days of use. Suppose that the cars have been categorized according to whether the card needs warranty- related repair( yes or no) and the country in which the company manufacturing the car is based ( united states or not united states)Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car is manufactured by...
Journal Entries for Plant Assets During the first few days of the year, Jules Company entered...
Journal Entries for Plant Assets During the first few days of the year, Jules Company entered into the following transactions: 1 Purchased a parcel of land with a building on it for $900,000 cash. The building, which will be used in operations, has an estimated useful life of 20 years and a salvage value of $60,000. The assessed valuations for property tax purposes show the land at $80,000 and the building at $720,000. 2 Paid $31,200 for the construction of...
During the performance, someone's cell phone rings in the audience at a volume of 60 dB....
During the performance, someone's cell phone rings in the audience at a volume of 60 dB. How many times louder is the orchestra than the sound of the cell phone ringing? Show your work. (5 points) C. A few weeks later, you attend a rock concert at which the band plays at 110 dB. How many times more intense is the rock concert than the orchestra concert? Show your work. (5 points) 3. The electromagnetic spectrum includes a number of...
Data: Fuel economy ratings for different cars. OLD:   16        27        17        33 NEW: 15        24&
Data: Fuel economy ratings for different cars. OLD:   16        27        17        33 NEW: 15        24        12        29 Is there a linear correlation between old ratings and new ratings and explain why. Use an α = 0.05 significance level. The critical value of the Pearson Correlation Coefficient r is 0.950 (for n = 4 and α = 0.05).
If during the first year of the new administration, American students organize a boycott of clothing...
If during the first year of the new administration, American students organize a boycott of clothing produced in foreign ‘sweat shops’ and Immigration of workers suitable for employment in the clothing market slows. Explain the long-term effects each will have on both wages and employment levels in the domestic clothing labor market?
Explain the reason for each Performance Standard of first aid for an adult: Performance Standard Rationale...
Explain the reason for each Performance Standard of first aid for an adult: Performance Standard Rationale Assess and Activation: Scene safety Example: -pause and look at the person and the scene before responding ASSESSES: Checks for responsiveness, pulse and breathing (or no breathing, abnormal breathing, or only gasping) at least 5 seconds no more than 10 seconds. ACTIVATES emergency response system and send someone to get the AED GIVES HIGH-QUALITY CPR: starts with compressions Hand Placement Adequate Rate (100 to...
Suppose during the first year of the new administration, several events occur: • Wages in market...
Suppose during the first year of the new administration, several events occur: • Wages in market X - which requires workers with the same traits and skills as workers in the clothing market – rise • American students organize a boycott of clothing produced in foreign ‘sweat shops’. - Briefly explain the long-term effects each will have on both wages and employment levels in the domestic clothing labor market?
1) As you plan for a new corporate project, you find that during the first year...
1) As you plan for a new corporate project, you find that during the first year of the project's life the expectation is that revenues will total $100,000, variable costs will be 60% of revenues, fixed costs will be $30,000, and depreciation will be $10,000. Given a corporate tax rate of 40%, find the free cash-flow for the first year of the project. Enter your number in dollars, with no decimals. 2) Same as for the question above, you plan...
The following transactions occurred during the first year of operations for Cougar Corp. for each transaction...
The following transactions occurred during the first year of operations for Cougar Corp. for each transaction prepare the year-end adjusting journal entry. Note: these ARE adjusting entries. a. Cougar Corp. purchased $4,300 in supplies during the year. A count at the end of the year showed that $650 of the supplies are still on hand. b. Cougar Corp. needs to record depreciation for its Vehicles. The depreciation amount is $4,100. c. Cougar Corp. owes its employees $5,700 for work performed...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT