   Chapter 8.4, Problem 42E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Inventory Suppose that the electrical supplies distributor in Example 6 wants to reduce its daily inventory but wants to limit to 5% the number of days it will have an insufficient inventory of 48-in. fluorescent lightbulbs to meet daily demand. At what level should it maintain its daily inventory? (Recall that the daily demand over the past year had a mean of 432 and a standard deviation of 86.1.)

To determine

To calculate: The level should it maintain its daily inventory. Suppose that the electrical supplies distributor in Example 6 wants to reduce its daily inventory but wants to limit to 5% the number of days it will have an insufficient inventory of 48-in. fluorescent lightbulbs to meet daily demand. The daily demand over the past year had a mean of 432 and a standard deviation of 86.1.

Explanation

Given Information:

Suppose that the electrical supplies distributor in Example 6 wants to reduce its daily inventory but wants to limit to 5% the number of days it will have an insufficient inventory of 48-in. fluorescent lightbulbs to meet daily demand. The daily demand over the past year had a mean of 432 and a standard deviation of 86.1.

Formula used:

If data for a population are normally distributed and σ is the standard deviation of the population data, then the number of standard deviations that x is from the mean μ is given by the z-score as;

z=xμσ

Calculation:

Consider that the electrical supplies distributor wants to reduce the daily inventory and wants to limit to 5% the number of days that it will have an insufficient inventory of 48-in.

Hence the probability condition is;

Pr(zxμσ)=0.05

Hence the distribution is normal.

The mean and standard deviation is;

μ=432σ=86.1

Thus one can have,

Pr(zx43286

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