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 0.18. 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. (a) p(make your first sale on the fifth call) = 0.081 (round to three decimal places as needed.) (b) p(make your first sale on the first, second, or third call) = 0.449 (round to three decimal places as needed.) (c) p(do not make a sale on the first three calls) = 0.551 (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: Recall the rule for unusual events

An event is considered unusual if its probability is less than or equal to 0.05 (or 5%).

Step2: Analyze each event's probability

• For part (a): \( P(\text{make first sale on fifth call}) = 0.081 \). Since \( 0.081> 0.05 \), this event is not unusual.
• For part (b): \( P(\text{make first sale on first, second, or third call}) = 0.449 \). Since \( 0.449>0.05 \), this event is not unusual.
• For part (c): \( P(\text{do not make a sale on first three calls}) = 0.551 \). Since \( 0.551 > 0.05 \), this event is not unusual.

Step3: Determine the correct option

Since none of the events have a probability ≤ 0.05, none of the events are unusual.

Answer:

D. None of the events are unusual.