The average number of unclaimed results in a day is 5, which means that the Poisson parameter λ = 5. The Poisson distribution is used to model the probability of a given number of events occurring in a fixed interval of time or space, assuming that these events occur independently of each other and at a constant rate.
The probability of observing 3 unclaimed results in a day can be calculated using the Poisson probability mass function:
P(X = 3) = (e^(-λ) * λ^x) / x!
where X is the number of unclaimed results in a day, λ = 5, and x = 3.
Plugging in these values, we get:
P(X = 3) = (e^(-5) * 5^3) / 3! ≈ 0.140
Therefore, the probability that the laboratory will observe 3 unclaimed results in a day is approximately 0.140 or 14.0%.