Cashback Offer (15th - 25th November 2020). Get Flat 10% Cashback credited in your account on a minimum transaction of $80. Post Your Question

Question DetailsNormal
$ 15.00

Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally

Question posted by
Online Tutor Profile
request

Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!

Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?

 

***This is a forum question, so **Please explain how you were able to come to the answer**.  Similarly to the way the answer is explained below.  There is no need for any type of table. Please provide the answer in a word document.***

 

To determine the probability that a company will run out of units we will let Y equal the demand for three weeks by establishing the mean.

 

(Y) = 3 week period

(Y) = 50+45+65 = 160 (Mean)

 

Next we need to find the variance by squaring the standard deviations and adding them together.

 

Variance (3 week) = 10^2 + 5^2 + 15^2 = 350

 

Next determine the standard deviation (SD) of the three week interval but utilizing the square root of the variant.

 

SD of 3 week interval = square root(350) = 18.7 = SD

 

Information calculated thus far:

 

mean = 160

Variance = 350

Standard deviation = 18.7  

 

Z score = ( value-mean ) / Standard Deviation

 

Using the above formula we come up with the following:

 

Z score = (180-160) / 18.7 = 1.07

 

Using the normal distribution table, if we look up 1.07 we get the result of .8577, which translates to 85.77%.  

 

To find out the probability of the company running out of their stock if they don’t receive a shipment from its supplier for three weeks use the following equation:

 

100% - 85.77% = 14.23%

 

Based on the given information, 14.23% of the time the company will run out of stock if it doesn't receive a shipment from its supplier for three weeks.

 

Available Answer
$ 15.00

[Solved] Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally

  • This solution is not purchased yet.
  • Submitted On 22 Oct, 2017 09:29:55
Answer posted by
Online Tutor Profile
solution
Suppose that the deman...
Buy now to view the complete solution
Other Similar Questions
User Profile
NUMBE...

Suppose that the population of the scores of all high school seniors who took the SAT Math test A++

Art 1:  Multiple Choice.  Circle the letter corresponding to the best answer. (Z*)() = 25.76     Z* = 2.576 Normalcdf(-2.576, 2.576, 0,1) = 0.99 in the middle with 0.005 in each tail. 1.   Suppose that the ...
User Profile
Beam7...

Suppose there are two Biostatistics classes of 18 students and 12 students

Please see attached Thank you!...........................
User Profile
Beam7...

Suppose that we have found that in Jill's remote log-ins to a certain computer

Please see attached Thank you!...........................
User Profile
Beam7...

Suppose the population fraction of people without a certain disease

Please see attached Thank you!.........................
User Profile
Beam7...

Suppose that 30 percent of the bottles produced in a certain plant are defective

Please see attached Thank you!.........................

The benefits of buying study notes from CourseMerit

homeworkhelptime
Assurance Of Timely Delivery
We value your patience, and to ensure you always receive your homework help within the promised time, our dedicated team of tutors begins their work as soon as the request arrives.
tutoring
Best Price In The Market
All the services that are available on our page cost only a nominal amount of money. In fact, the prices are lower than the industry standards. You can always expect value for money from us.
tutorsupport
Uninterrupted 24/7 Support
Our customer support wing remains online 24x7 to provide you seamless assistance. Also, when you post a query or a request here, you can expect an immediate response from our side.
closebutton

$ 629.35