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# Probability and Statistics

1. For this question pretend you are drawing cards without replacement from the infamous "Iraq's Most Wanted" deck issued by the U.S. Military. If you are drawing from the full deck of 55 cards, what are the following probabilities:

a. You draw a card that is not Saddam Hussein
b. You draw two cards, which end up being Saddam Hussein and another one with his cousin "Chemical Ali"
c. You draw 14 cards and not one of them is Saddam Hussein = I need help with this one!

2. You have administered a standardized test of manual dexterity to two groups of 10 semi skilled workers. One of these two groups of workers will be employed by you to work in a warehouse with many fragile items. The higher the manual dexterity of a worker the less likelihood that worker will break significant inventory. Because of a unique contract you must hire all 10 employees from one of the two groups and none of the employees from the other.

Group A - 98,85,30,66,99,95,57,62,99,100
Group B - 64,81,62,88,82,79,91,81,85,78

You must decide which group to choose. Choose at least two measures of central tendency and at least one measure of dispersion for each group and use those to make your choice. Be sure to justify your choice with at least one page of discussion and analysis.

I would choose Group B, The mean is 79.1, mode is 82+79/2=80.5; do you agree? I'm not sure how to get one measure of dispersion

3. You are the production manager for an operation that produces circuit boards. Each board is tested at the end of the manufacturing process. Rejected boards are discarded and have no future value. For product B-17, you have kept data on the number of rejects for the past 38 weeks. These data are found in this Excel spreadsheet. (see attachment)

Prepare a frequency distribution chart.
Does this approximate a normal curve?
What is the Standard Deviation (use Excel to calculate this value with the STDEV function)?
What is the approximate probability that at least 7 rejected boards will be produced next week?

#### Solution Preview

1. For this question pretend you are drawing cards without replacement from the infamous "Iraq's Most Wanted" deck issued by the U.S. Military. If you are drawing from the full deck of 55 cards, what are the following probabilities:

a. You draw a card that is not Saddam Hussein, = 51 out of 55

This is correct. Assuming there are 4 Saddam's (he is the "king"), there are 55 - 4 = 51 non-Saddam's. Therefore, the probability that you draw a non-Saddam is 51/55 = 0.927 = 92.7%.

b. You draw two cards, which end up being Saddam Hussein and another one with his cousin "Chemical Ali". = 8 out of 55

This is incorrect - you have found the probability that you draw one card and it is either Saddam or Ali. The probability that you draw Saddam is 4/55. Now, there are 54 cards remaining. The probability that you draw Ali is now 4/54. The probability of both of these events happening is (4/55)(4/54) = 16/2970 = 0.005 = 0.5%

c. You draw 14 cards and not one of them is Saddam Hussein = help with this one

We have established that the probability of drawing one card that is not Saddam is 51/55. Now there are 54 cards left. The probability of drawing another non-Saddam is 50/54. Now there are 53 cards. The probability of drawing another non-Saddam is 49/53. Continue in this manner and multiply the ...

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