Most software manufacturers offer a help line that allows consumers to call and

Question

Most software manufacturers offer a help line that allows consumers to call and receive assistance in solving their problems. However, because of the volume of calls, customers frequently are put on hold. One software manufacturer claims that only 20% of callers are put on hold. Suppose that 100 customers call. 1. What is the probability distribution of the random variable of interest? Justify your answer. 2. What is the probability that exactly 20 of them are put on hold? 3. What is the probability that more than 25 of them are put on hold?

Explanation / Answer

one customer can be put on hold or may be answered

so teo outcomes success and failures

so The random variable follows BINOMIAL distributions

X~BINOMIAL(100,.2)

P(X=20)= dbinom(20,100,.2)=0.09930021

c)P(X>25)

approximately X~POISSON(100*.2=20)=0.112185

without approximation

1-pbinom(25,100,0.2)= 0.08747538

one can also standardise and use NORMAL APPROXIMATION

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