The Excel file Call Center Data shows that in a sample of 70 individuals, 27 had prior call center experience. If we assume that the probability that any potential hire will also have experience with a probability of 2770, what is the probability that among 10 potential hires, more than half of them will have experience? Define the parameter(s) for this distribution based on the data.

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The Excel file Call Center Data shows that in a sample of 70 individuals, 27 had prior call center experience.   If we assume that the probability that any potential hire will also have experience with a probability of 2770, what is the probability that among 10 potential hires, more than half of them will have experience? Define the parameter(s) for this distribution based on the data.

Jenny Bolton · Accepted Answer

Step 1  Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials being independent and the probability of success, say p, remaining constant, then the distribution of the number of success follows binomial.  Let us assume X be a random variable denoting the number of success.  Then X∼b∈(n,p), n and p being the parameters of the binomial distribution.  The probability mass function of X is given by,  P(X=x)={(nx)px(1−p)n−x,x=0,1,2,...,0,otherwise  Step 2  Let us assume X is a random variable denoting the number of hired people having experience out of 10 people  Here,  i) all the hired people are independent  ii) for each hired person, there are two possibilities - the person has experience (success) or not (failure)  iii) the probability for a person having experience remains constant for all hires  Under these conditions we can say that  X∼b∈(n,p)  with n=10,p=2770  Therefore, the probability that among 10 potential hires, more than half i.e. more than 5 of them will have experience is  P(X&amp;gt;5)=P(X≥6)  =∑x=610(10x)(2770)x(1−2770)10−x  =0.09847+0.03533+0.00832+0.00116+0.00007  =0.1434 (rounded to 4 decimal places)  Answer: The probability that among 10 potential hires, more than half of them will have experience is 0.1434.

The Excel file Call Center Data shows that in a sample of 70 individua

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