MATH 125 Unit 4 Individual ProjectAnswer Form Counting Techniques and Introduction to Probability

MATH125: Unit 4 Individual Project

ANSWER FORM

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• In how many ways can 5 states be selected from the top 10 states with the most murders if the order of the 5 statesmatters?
• In how many ways can 5 states be selected from the top 10 states with the most murders if the order of the 5 states does not matter?

10P3=10! / (10-3)! = 10! / 7! = 10*9*8*7! / 7! = 10*9*8= 720

10C3= 10! / (10-3)! * 3! = 10! / 7! * 3! = 10*9*8*7! / 7! * 3*2*1 = 720 / 6 = 120

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• What would be the probability that randomly choosing 3 states from the top 6 murder states would actually be the top 3 states for murders in the United States in exact correct decreasing order (1. CA, 2. TX, 3. NY)?

6P3= 6! / (6! – 3!) = 6! / 3! = 6*5*4*3! /3*2*1 = 6*5*4 = 120

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• Find the top 20 states with the most number of total murders. Then, calculate the mean, median, and mode.

Mean: 1790+1089+774+636+613+522+489+488+485+452+398+379+373+364+339+319+303+284+204+187 / 20 = 10488 / 20 =524.4

Median: 452+398 / 2 = 850 / 2 = 425

Mode: For this data set, there is not any reoccurring number, therefore, there is no mode.

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• Calculate the variance and standard deviation for the top 20 states with the most number of total murders.

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• Range: 1790 – 187 = 1603
• Variance: (1790-1603)2+(1089-1603)2+(774-1603)2+(636-1603)2+(613-1603)2+(522-1603)2+(489-1603)2+(488-1603)2+(485-1603)2+(452-1603)2+(398-1603)2+(379+1603)2+(373-1603)2+(364-1603)2+(339-1603)2+(319-1603)2+(303-1603)2+(284-1603)2+(204-1603)2+(187-1603)2 / 20-1= 34969+264196+687241+935089+980100+1168561+1240996+1243225+1249924+1324801+1452025+1498176+1512900+1535121+1597696+1648656+1690000+1739761+1957201+2005056 / 20-1 = 25765694 / 19 = 1356089.16
• Standard Deviation: = 362.6
• In Texas, given that a specific person was murdered by a firearm, what is the probability that the murder was committed with a rifle?

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• 4 / 699 = 0.0057
• In California, given that a specific person was murdered by a firearm, what is the probability that the murder was committed either with a rifle or a shotgun?

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• 45 + 50 = 95 / 1220 = 0.078
• Choose 2 states, and determine how many more times likely a person is to be murdered using a handgun in one state compared to the other state if the person is murdered.

Alaska: 5 / 16 = 0.31 = 31 / 100 = 31%

Arizona: 165 / 222 = 0.74 / 100 = 74%

Explain your answer below

• For what reasons do you think California and Texas seemingly had a disproportionate number of murders than New York and Pennsylvania in 2011? Please do your research and include the references that support your answer.

Reference: