# HW 4 -...

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Three different experiments are presented in the following grid. For each experiment, select whether or not  the binomial distribution could represent the outcomes. Yes No a) Ten companies are chosen at random and it is recorded whether the employee base of each company is growing, shrinking or stable. b) An office has 20 staff, of which 25% are female. Ten of the staff are chosen at random to give a presentation. For each of the 10 chosen staff members, an observer records whether or not they are female. c) Lee the barista has a 95% chance of making and serving a coffee within 3 minutes of the order being placed, and the time it takes to serve a coffee is independent of the time it takes to serve any other coffee. Lee is observed by his boss for the next 10 orders, and the boss records how many times Lee completes the order within 3 minutes. [3 out of 3] -       Feedback a) You are correct. b) You are correct. c) You are correct. Discussion a) Each trial in this experiment may produce three results: growing, shrinking or stable. If an experiment has  repeated trials, the binomial distribution will only apply if each trial will produce exactly two results, often  denoted success and failure. Therefore the binomial distribution would not apply to this experiment as it is. Note that if instead it were simply recorded whether or not the employee base was growing, this experiment  could be represented by the binomial distribution. In this case growing would be considered a success and  not growing would be considered a failure. b) This experiment could not be represented by the binomial distribution because the trials are not  independent. This is because there is only a finite number of staff from which the 10 are randomly chosen. Since 25% of the 20 total staff are female, there are 5 females in the 20 total staff. Suppose, for example,  that the observer notes that the first of the 10 chosen staff is a female. There is a 25% chance of this,  because 25% of the staff are female. However, now there are only 4 females left (and 19 total staff members  left). So in looking at the second of the 10 chosen staff, there is only a 4/19 = 21.05%   chance that this staff  member is female. In other words, the fact that the first of the 10 chosen staff is female causes the probability that other chosen  staff members are female to decrease. The reason for this is that there are only finitely many females to

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begin with, and therefore when one 'trial' results in a female, the probability that later trials will result in  female is decreased. The binomial distribution assumes that all trials are independent, and therefore does not apply to this
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## This note was uploaded on 09/29/2011 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue University-West Lafayette.

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HW 4 -...

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