Question

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 0.11. find the probability that you (a) make your first sale on the fifth call, (b) make your first sale on the first, second, or third call, and (c) do not make a sale on the first three calls. (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 first 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.

Explanation:

Step1: Calculate probability for part (a)

The geometric distribution formula is \(P(X = k)=(1 - p)^{k - 1}p\), where \(p = 0.11\) and \(k = 5\).

$$
LATEXBLOCK0
$$

Step2: Calculate probability for part (b)

\(P(X=1)+P(X = 2)+P(X=3)\)

$$
LATEXBLOCK1
$$

Step3: Calculate probability for part (c)

\(P(X>3)=(1 - p)^{3}\), where \(p = 0.11\)

$$
LATEXBLOCK2
$$

Step4: Determine unusual events

An event is unusual if \(P\leq0.05\). Since \(0.069>0.05\), \(0.295>0.05\), \(0.705>0.05\)

Answer:

D. None of the events are unusual.