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IE 151: Homework 2 Spring 2014

New Mexico State University

Department of Industrial Engineering

Due Thursday, February 13 th

at 11:55PM

Section 1: Probability (Show all work in Microsoft Word) – 8 points

For this problem consider the following situation. In a bag we have a total of 11 marbles. 4 are red, 3 are

blue, 2 are green, and 2 are black. Answer the following questions; use the formulas from probability which

we used in class.

a) What is the probability of pulling a red marble from the bag? b) What is the probability of pulling either a green or a black marble from the bag? c) How many marbles would you have to pull to guarantee that you have pulled at least one blue

marble?

d) How much more probable are you to pull a green marble now if you add 2 more green marbles to the bag?

e) If the red marbles were half the size of the green marbles, would the probability of pulling a red or a green marble be the same? Defend your answer

f) If I add one more of each marble, are the new and the old probabilities equal?

Continued on next page…

Section 2: Normal Distribution (Show all work in Microsoft Word) – 12 points

Little did you know, but Charlie Bucket from Willy Wonka and the Chocolate factory was an Industrial

Engineer. The real reason he was selected amongst the other participants was to optimize the way the

factory was run. His first project was to optimize the way that the good and bad eggs are determined. Willy

has known for some time that unfortunately a number of good eggs have been misclassified as bad eggs.

Currently the only way that good and bad eggs are separated is by weight. Charlie’s job is to determine if the

weight alone should be the only determining factor when finding a bad egg. The company policy currently

states: “Bad eggs come in two sizes, both contain horrible surprises, the good part is missing from one, in the

other bad is added for fun.” This translates to bad eggs weigh both more and less than good eggs.

The following table shows 50 good eggs.

Good Eggs

Egg Weight Egg Weight Egg Weight Egg Weight Egg Weight

1 39.28 11 34.52 21 35.90 31 31.73 41 41.21

2 30.35 12 29.63 22 35.62 32 33.94 42 37.96

3 33.04 13 32.92 23 33.88 33 35.72 43 35.78

4 36.10 14 35.53 24 34.66 34 35.81 44 35.39

5 31.36 15 35.82 25 33.91 35 29.12 45 35.86

6 36.44 16 34.25 26 38.93 36 32.90 46 32.14

7 33.65 17 35.75 27 37.30 37 33.67 47 37.65

8 33.58 18 34.77 28 30.31 38 34.72 48 35.30

9 37.80 19 35.96 29 34.57 39 36.63 49 37.56

10 37.17 20 33.44 30 38.92 40 36.78 50 33.41

A) What is being measured in this problem B) Is this a continuous or discrete distribution and why? C) Devise a method of randomly sampling from this group of good eggs. Charlie would like work with a

sample size of 10 eggs. Describe in detail how Charlie will be selecting the ten eggs for his sample.

D) Report the sample that Charlie used E) Sketch this normal distribution accurately using what we know about ��. Bonus (+2) if you plot

using excel.

F) Below is a table of 12 bad eggs, plot these eggs on the normal distribution above using red dots.

Bad Eggs

Egg Weight Egg Weight

1 41.00 7 27.65

2 40.20 8 28.85

3 39.20 9 30.24

4 29.80 10 23.25

5 29.00 11 42.80

6 39.99 12 43.11

G) What is your conclusion about whether or not the weight is enough evidence of a good or bad egg? Use the knowledge we have learned in the class to defend your answer.