A mountain search and rescue team received an average of 600 calls per year. Use the poisson dustribution to find the probability that on a randomly selected day, they will receive 1 or more calls.
To find the probability that on a randomly selected day, the mountain search and rescue team will receive 1 or more calls, we can use the Poisson distribution formula.
The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space. It is characterized by a single parameter, λ (lambda), which represents the average number of events that occur in the given interval.
In this case, we are given that the team receives an average of 600 calls per year. To convert this average to the average number of calls per day, we divide 600 by the number of days in a year. Let's assume there are 365 days in a year:
Average number of calls per day = 600 / 365 ≈ 1.64
Now, we can use the Poisson distribution formula to find the probability of getting 1 or more calls on a randomly selected day. The formula is as follows:
P(X ≥ 1) = 1 - P(X = 0) = 1 - e^(-λ)
Where:
P(X ≥ 1) is the probability of getting 1 or more calls,
P(X = 0) is the probability of getting exactly 0 calls, and
e is Euler's number (approximately 2.71828).
Substituting the value of λ into the formula:
P(X ≥ 1) = 1 - e^(-1.64)
Calculating this expression gives us the probability that on a randomly selected day, the team will receive 1 or more calls.