Question

A kaya-rental company needs to replace many of its kayaks, and it wants to ensure it has enough kayaks to meet the demand from customers during the summer season. On average, it rents out 42 kayaks. Find the probability that the company will have enough kayaks on any given day. Round the answer to the nearest tenth.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the probability that the company will have enough kayaks on any given day, we need to calculate the probability of having at least 42 kayaks available.

Let's assume the number of kayaks available follows a Poisson distribution with a mean of 42.

Using the Poisson probability formula:

P(x ≥ 42) = 1 - P(x < 42)

P(x < 42) = Σ(e^(-42) * (42^k) / k!)

where k ranges from 0 to 41.

Calculating the Poisson probability:

P(x < 42) ≈ Σ(e^(-42) * (42^k) / k!) from k=0 to 41

P(x < 42) ≈ Σ(e^(-42) * (42^k) / k!) from k=0 to 41 = 0.889

Therefore, the probability of having enough kayaks on any given day is:

P(x ≥ 42) = 1 - P(x < 42) = 1 - 0.889 = 0.111

Rounded to the nearest tenth, the probability of having enough kayaks on any given day is approximately 0.1 or 10.1%.