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A telemarketer, who places random phone calls to potential customers,  has a .05 probability of making a...

A telemarketer, who places random phone calls to potential customers,  has a .05 probability of making a sale with every phone call, independently of other phone calls. What is the expected number of calls needed to make the first sale of a day? What is the probability that more than 10 calls will be needed to make the first sale of the day?

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Answer #1

1)

Expected number of calls needed to make the first sale of day is given by below formula

Using the geometric distribution

Probability of making sale with every phone call

Probability of not making sale with every phone call

2)

We have to find the probability that more than 10 calls will be needed to make the first sale of the day

Let X denotes the number of failures calls in which no sales were done

X-geometric p

Using the definition of PDF of X

when

Let us find the probability that more than 10 calls will be needed to make the first sale of the day

=1-[0.05+0.0475+0.045125+0.04289+0.040725+0.036755+0.0349+0.0331+0.03151]

=1-[0.444]

=0.556

probability that more than 10 calls will be needed to make the first sale of the day will be 0.556

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