Question

In: Statistics and Probability

A car saleswoman has worked for the same car sales company for many years. Based on...

A car saleswoman has worked for the same car sales company for many years. Based on her track record, her selling prices of cars can be modelled by a normal distribution with mean $12,000AUD with standard deviation $2,000AUD. (a.) What is the probability that the car saleswoman sells a car that is more expensive than $13,500AUD? (b.) During a given month, 14 customers buy a car from her. What is the probability that at least 3 of them bought a car that is cheaper than $13,500AUD? Carefully state the assumptions of your solution. (c.) The car saleswoman has a bonus plan that entitles her to a bonus if she sells 4 cars that each costs $13,500AUD or more during a month. What is the probability that she receives the bonus when the 8th car of the month is sold?

Solutions

Expert Solution

a)

µ =    12000                  
σ =    2000                  
                      
P ( X ≥   13500.00   ) = P( (X-µ)/σ ≥ (13500-12000) / 2000)              
= P(Z ≥   0.750   ) = P( Z <   -0.750   ) =    0.2266   (answer)

b)

Probability of cheaper than 13500

µ =    12000      
σ =    2000      
          
P( X ≤    13500   ) = P( (X-µ)/σ ≤ (13500-12000) /2000)  
=P(Z ≤   0.750   ) =   0.7734

Now applying binomial

X P(X)
P ( X = 0) = C (14,0) * 0.773372647623132^0 * ( 1 - 0.773372647623132)^14= 0 0.0000000
P ( X = 1) = C (14,1) * 0.773372647623132^1 * ( 1 - 0.773372647623132)^13= 1 0.0000000
P ( X = 2) = C (14,2) * 0.773372647623132^2 * ( 1 - 0.773372647623132)^12= 2 0.0000010

P(X>=3) = 1 - P(X<=2)

= 0.9999

c)

Sample size , n =    7
Probability of an event of interest, p =   0.2266

X P(X)
P ( X = 3) = C (7,3) * 0.226627352376868^3 * ( 1 - 0.226627352376868)^4= 3 0.1457

Probability = 0.1457 * 0.2266

= 0.033

Thanks in advance!

revert back for doubt

Please upvote


Related Solutions

A car saleswoman has worked for the same car sales company for many years. Based on...
A car saleswoman has worked for the same car sales company for many years. Based on her track record, her selling prices of cars can be modelled by a normal distribution with mean $12,000AUD with standard deviation $2,000AUD. (a.) What is the probability that the car saleswoman sells a car that is more expensive than $13,500AUD? (b.) During a given month, 14 customers buy a car from her. What is the probability that at least 3 of them bought a...
A study compared the number of years a person has worked for the same company (X)...
A study compared the number of years a person has worked for the same company (X) with the person’s salary in thousands of dollars per year (Y). The data for nine employees appear in the following table. Use the data to answer the questions. Years Annual Salary 5 24 8 40 3 20 6 30 4 50 9 40 7 35 10 50 Answer these questions based on the research scenario and the data in this table. What is the...
Hazel had worked for the same Fortune 500 company for almost 15 years. Although the company...
Hazel had worked for the same Fortune 500 company for almost 15 years. Although the company had gone through some tough times, things were starting to turn around. Customer orders were up, and quality and productivity had improved dramatically from what they had been only a few years earlier due to a company wide quality improvements program. So it came as a real shock to Hazel and about 400 of her coworkers when they were suddenly terminated following the new...
QUESTION TWO A teacher has worked in the same primary school for two years. While chatting...
QUESTION TWO A teacher has worked in the same primary school for two years. While chatting to the children, she is concerned to find that the majority of them come to school without having eaten a healthy breakfast. In her opinion, children who eat ‘a decent breakfast’learn to read more quickly and are better behaved than children who do not. She now wants to set up a pre-school breakfast club for the children so that they can all have this...
SHEENA Sheena had worked for the same Fortune 500 Company for most 15 years. Although the...
SHEENA Sheena had worked for the same Fortune 500 Company for most 15 years. Although the company had gone through some tough times, things were starting to turn around. Customer orders were up, and quality and productivity had improved dramatically from what they had been only a few years earlier due companywide quality improvement program. So, it comes as a real shock to Sheena and about 400 of her co-workers when they were suddenly terminated following the new CEO’s decision...
c) A Business Analyst has worked for Snoopy Insurance Ltd. for many years.  Her contract had a...
c) A Business Analyst has worked for Snoopy Insurance Ltd. for many years.  Her contract had a term of Post-Employment Limitations: not to work for a competitor for 1 year after quitting her job.  This term was to protect the company from revealing any business secrets.   Later, she left the insurance company and immediately joined a software vendor, which develops and sells a computer system for insurance to her former company. Does she violate legal or ethical issues?  Would there be any conflict of...
Leon has worked for a small tool and die company for several years. The owner is...
Leon has worked for a small tool and die company for several years. The owner is retiring and Leon has the opportunity to purchase the business. However, he plans to retire in 10 years, and he knows that neither of his children has any desire to work in the business. What appears to be Leon’s key consideration in choosing an ownership structure? a. Business control and transfer of ownership b. Ease of start-up and administration c. Management structure d. Legal...
Hanjuan Jin, a citizen of China, worked as a software engineer for Motorola for many years...
Hanjuan Jin, a citizen of China, worked as a software engineer for Motorola for many years in a division that created proprietary standards for cellular communications. Contrary to Motorola’s policies, Jin also secretly began working as a consultant for Lemko Corp., as well as with Sun Kaisens, a Chinese software company, and with the Chinese military. She started corresponding with Sun Kaisens’s management about a possible full-time job in China. Jin took several medical leaves of absence from Motorola to...
3. Quickstart company makes 12-volt car batteries. After many years of testing, the company knows that...
3. Quickstart company makes 12-volt car batteries. After many years of testing, the company knows that the average life of a quick start battery is normally distributed, with a mean if 45 months and a standard deviation of 8 months. A. If Quickstart company guarantees a full refund on any battery that fails within 36 months after purchase, what of its batteries will the company expect to replace? (Round to a whole percentage) B. If Quickstart company only wants to...
Donald is in the market for a used car. He has found the same sports car...
Donald is in the market for a used car. He has found the same sports car at two different dealerships and is now considering which dealer he should purchase the car from. Dealer 1 requires Donald to get the loan through their lending department. Dealer 1 has told Donald that because they do their own financing, they can get Donald the very best loan possible and Donaldwill only have to pay $365 per month for 60 months (5 years). Dealer...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT