MidtermExam1_2008_Solutions

MidtermExam1_2008_Solutions - CHEN 3010 Applied Data...

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CHEN 3010 Applied Data Analysis Fall 2008 Name:________________________________ Midterm Examination 1 Solutions 1) (10 pts) A portable communications radio uses 4 AA batteries but can be powered successfully using either 4 fresh batteries or a combination of 3 fresh batteries and 1 dead battery. There is a collection of 20 AA batteries randomly mixed in a drawer, and 7 of those batteries are dead. What is the probability that a selection of 4 batteries from the drawer, when installed in the radio, will power the radio successfully? Solution: We want to find the total number of combinations of batteries that will power the radio successfully. Then, we can determine the probability that a combination of 4 batteries will power the radio by: P = (# of combinations that will power the radio)/(total # of 4-battery combinations) The number of combinations that will power the radio is composed of combinations that are composed of: 1) 3 fresh batteries and one old battery or 2) 4 fresh batteries. 3 fresh/1 old: = 2002 1 7 3 13 = C C 4 fresh: = 715 4 13 = C Total # of combinations = 4845 4 20 = C Therefore, the probability of picking a combination of working batteries is: 561 . 0 4845 715 2002 ] [ = + = working P or about 56% 2) (10 pts) Rats are tested in a laboratory by injection of a new drug that inhibits the synthesis of a protein. The probability that a rat will die from the drug before the experiment is complete is 0.05. If 50 rats are injected with the drug, what is the probability that at least 48 will survive? Solution: This is a cumulative binomial problem. The probability that exactly x number of rats will survive is ݂ሺݔሻ ൌ ቀ 50 ݔ ቁ 0.95 0.05 ହ଴ି௫ . So, the probability that at least 48 will survive is: ܲሾܺ൒48ሿ ൌ ቀ 50 48 ቁ 0.95 ସ଼ 0.05 ൅ ቀ 50 49 ቁ 0.95 ସଽ 0.05 ൅ ቀ 50 50 ቁ 0.95 ହ଴ 0.05 ൌ ૙. ૞૝૚ 3) (20 pts) A trucking company operates a large fleet of trucks and last year they had 103 breakdowns. Multiple breakdowns can occur on a single day.
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This note was uploaded on 04/25/2010 for the course CHEN 3010 at Colorado.

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MidtermExam1_2008_Solutions - CHEN 3010 Applied Data...

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