Problem

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. Assume the probability that you will make a sale on any given telephone call is 0.14 . Find the probability that you (a) make your first sale on the fifth call, (b) make your sale on the first, second, or third call, and (c) do not make a sale on the first three calls. (c) $P$ (do not make a sale on the first three calls) $=0.636$ (Round to three decimal places as needed.) Which of the events are unusual? Select all that apply. A. The event in part (a), "make your first sale on the fifth call", is unusual. B. The event in part (b), "make your sale on the first, second, or third call", is unusual. C. The event in part (c), "do not make a sale on the first three calls", is unusual. D. None of the events are unusual.

Solution

Step 1 :We are given that the probability of making a sale on any given call is 0.14. The events are independent, meaning each call does not affect the outcome of the others. This is a geometric distribution problem.

Step 2 :For part (a), we need to find the probability that the first success (sale) occurs on the fifth call. This means that the first four calls are failures (no sale) and the fifth call is a success. The probability for this event is approximately 0.077.

Step 3 :For part (b), we need to find the probability that the first success occurs on the first, second, or third call. This means we need to find the sum of the probabilities of a success on the first call, a success on the second call (after one failure), and a success on the third call (after two failures). The probability for this event is approximately 0.364.

Step 4 :For part (c), we need to find the probability that the first three calls are all failures (no sale). The probability for this event is approximately 0.636.

Step 5 :An event is considered unusual if its probability is less than or equal to 0.05. Comparing the probabilities of the events to this threshold, we can see that none of the events are unusual.

Step 6 :Final Answer: \(\boxed{\text{D. None of the events are unusual}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/17428/

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