Problem set 3

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University of Maryland Global Campus (UMGC) *

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105

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Statistics

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Feb 20, 2024

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docx

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Problem set 3 Question 1 Statistics: Mean and Median Refer to the chart below and the line associated with your assigned number to answer these questions. Using the 10 original numbers given for the data set and the listed change: (a) By how much does the mean decrease or increase, or does it stay the same? (b) By how much does the median decrease or increase, or does it stay the same? Assigned # Original Numbers in the Data Set One Number Change 9 347, 357, 377, 415, 428, 442, 451, 452, 560, 511 428 to 438 a) Original mean: 347+357+377+415+428+442+451+452+560+511= 4340/10 = 434 Adjusted mean: 347+357+377+415+438+442+451+452+560+511= 4350/10= 435 Mean increases by 1 b) Original median: 347, 357, 377, 415, 428, 442 , 451, 452, 511, 560 (428+442) / 2= 435 c) Modified median: 347, 357, 377, 415, 438, 442 , 451, 452, 511, 560 438+442) / 2= 440 Median increased by 5

Question 2 Probability: Likelihood An event is more likely when it has a greater probability of happening. Refer to the chart below and the line associated with your assigned number to answer these questions. There are two boxes containing only red and purple pens. A pen is randomly chosen from each box. 1. Which of these events is most likely to occur? a. Event 1: choosing a red pen from Box B. b. Event 2: choosing a purple pen from Box A. c. Event 3: choosing a red pen from Box A. 2. Which of these events is least likely to occur? a. Event 1: choosing a red pen from Box A. b. Event 2: choosing a purple pen from Box B. c. Event 3: choosing a red pen from Box B. 3. Name an event with either box A or box B where the probability would be 1. 4. Name an event with either box A or box B where the probability would be 0. 5. Name an event with either box A or box B where the probability would be 3. Assigned # Box A - purple pens Box A - red pens Box B - purple pens Box B - red pens 9 24 13 18 15 1 a= 15/33 b= 24/37 c= 13/37 24/37 > 15/33 > 13/37 B, event 2 is the most likely to occur 2 a= 13/37 b=18/33 c=15/33 13/37 < 15/33 < 18/33 a, Event 1 would be least likely to occur 3. Choosing either a red or purple pen from box A. 4. Choosing a green pen from box B 5. The probability of an event can not be higher than 1.

Question 3 Probability: Counting Answer the question that corresponds with your assigned number. In all these questions the order of the choices does not matter; the order is not taken into consideration nor is it relevant. We are counting a choice once if it has the same items no matter the order we choose them. Example: Choosing Joe, then Sid, then Henry, and then James is the same as choosing Sid, then James, then Henry, then Joe. So, for this question you must use the Combination rule for counting. 9. From a collection of 50 store customers, 3 are to be chosen to receive a special gift. How many groups of 3 customers are possible? nCr = n! / r!(n-r)! 50C3 = 50! / 3!(50-3)! = (50 x 49 x 48) / (3 x 2 x 1) 19,600 combinations

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