Question

5. An Internet retailer stocks a popular electronic toy at a central warehouse that supplies the eastern United States. Every week, the retailer makes a decision about how many units of the toy to stock. Suppose that the weekly demand for the toy is approximately normally distributed with a mean of 2,500 units and a standard deviation of 300 units. a. If the retailer wants to limit the probability of being out of stock of the electronic toy to no more than 2.5% in a week, how many units should the central warehouse stock? b. If the retailer has 2,750 units on hand at the start of the week, what is the probability that weekly demand will be greater than inventory? c. If the standard deviation of weekly demand for the toy increases from 300 units to 500 units, how many more toys would have to be stocked to ensure that the probability of weekly demand exceeding inventory is no more than 2.5%? Problem is a normal distribution problem, show steps on how to enter in Minitab.

          5. An Internet retailer stocks a popular electronic toy at a central warehouse that supplies the eastern United States. Every week, the retailer makes a decision about how many units of the toy to stock. Suppose that the weekly demand for the toy is approximately normally distributed with a mean of 2,500 units and a standard deviation of 300 units.

a. If the retailer wants to limit the probability of being out of stock of the electronic toy to no more than 2.5% in a week, how many units should the central warehouse stock?

b. If the retailer has 2,750 units on hand at the start of the week, what is the probability that weekly demand will be greater than inventory?

c. If the standard deviation of weekly demand for the toy increases from 300 units to 500 units, how many more toys would have to be stocked to ensure that the probability of weekly demand exceeding inventory is no more than 2.5%?

Problem is a normal distribution problem, show steps on how to enter in Minitab.

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Added by Kristen A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Adi S

09/20/2022

Step 1

To limit the probability of being out of stock to no more than 2.5%, we need to find the number of units that corresponds to the 97.5th percentile of the normal distribution (since we want to cover 100% - 2.5% = 97.5% of the demand). In Minitab, you can use the Show more…

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5. An Internet retailer stocks a popular electronic toy at a central warehouse that supplies the eastern United States. Every week, the retailer makes a decision about how many units of the toy to stock. Suppose that the weekly demand for the toy is approximately normally distributed with a mean of 2,500 units and a standard deviation of 300 units. a. If the retailer wants to limit the probability of being out of stock of the electronic toy to no more than 2.5% in a week, how many units should the central warehouse stock? b. If the retailer has 2,750 units on hand at the start of the week, what is the probability that weekly demand will be greater than inventory? c. If the standard deviation of weekly demand for the toy increases from 300 units to 500 units, how many more toys would have to be stocked to ensure that the probability of weekly demand exceeding inventory is no more than 2.5%? Problem is a normal distribution problem, show steps on how to enter in Minitab.

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Transcript

00:01 Let us represent x as the demand of a toy and it is given that x follows the normal distribution with the mean demand of mu equal to 2 ,500 units with the standard deviation of sigma equal to 300 units.

00:20 Now in part a we have to find the cutoff value for the stock such that the out of stocks.

00:30 Should be no more than 2 .5 percentage.

00:36 This implies we have to find the cutoff value for the top 2 .5 percentage of the data.

00:43 Now to find the z value for this top 2 .5 percentage, the excel formula of equal to n -o -r -m dot s dot, i and v, 1 minus the 2 .5 percentage has 0 .025.

01:00 Is used and the excel output is given below.

01:03 Now using the excel output, the z critical value for the top 2 .5 percentage is 1 .96.

01:12 Now the number of stocks should be stocked by a company is calculated as mu plus z into sigma, which is 2 ,500 plus the z value of 1 .96 into the standard deviation value of 300.

01:28 Now simplifying this gives the value of 308.

01:34 Thus, the company should have the stock of 3088 such that their out of stock is no more than 2 .5 %.

01:44 In part b, it is given that the company has the inventory of 2 ,750 stocks.

01:53 Now we have to find the probability that the demand is greater.

01:58 Than the inventory and this can be calculated as probability that the demand x is greater than the given inventory of 2 ,750 and this can be calculated as 1 minus probability that the demand x is less than 2 ,750 since normal is a semantic distribution and this can be written as 1 minus probability that to standardize the value x minus mu by sigma which is less than 2 ,750 minus 2 ,500 divided by standard deviation value of 300...

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