Answered: The Paramount Paper company produces…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 2CYU

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Question

The Paramount Paper company produces paper from wood

pulp ordered from a lumber products firm. The paper com-
pany’s daily demand for wood pulp is normally distributed,

with a mean of 9000 pounds and a standard deviation of
1900 pounds. Lead time is eight days. Determine the reorder
point if the paper company wants to limit the probability of a
stockout and work stoppage to 2%.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Given:

Mean $μ$ = 9000

Standard deviation $σ$ = 1900

Lead time = 8 days

Probability = 2% = 0.02

Formula Used:

Reorder point = Demand during lead time + Safety stock

= (Lead time in days) $\times$ (Demand per day) + Z $\times$ (Standard deviation) $\times$ (Lead time in days)^0.5

Step 2

Explanation:

For Z-value Using MS Excel

Risk region = 0.02

Non-risk region = 1-0.02 = 0.98

Z = 2.0537

Reorder point = Demand during lead time + Safety stock

= (Lead time in days) $\times$ (Demand per day) + Z $\times$ (Standard deviation) $\times$ (Lead time in days)^0.5

$= 9000 \times 8 + 2.05 \times 1900 \times 8^{0.5} = 72000 + 11016.7236 = 83016.72365 \approx 83017$

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