A math teacher observes that on the average 3 students came to their 8-9AM class late. The probability 5 students will be late in their 8-9AM class is ???
what is the asnwer?
To find the probability of 5 students being late in the 8-9AM class, we can use the concept of a Poisson distribution. A Poisson distribution is typically used to model the number of events occurring in a fixed interval of time or space, given the average rate of occurrence.
In this case, the average rate of occurrence is given as 3 students coming late to the 8-9AM class. This means that, on average, λ = 3 students arrive late during this time interval.
The probability mass function (PMF) of a Poisson distribution is given by the formula:
P(X=k) = (e^(-λ) * λ^k) / k!
Where:
- P(X=k) represents the probability of k events occurring
- e is Euler's number (approximately 2.71828)
- λ is the average rate of occurrence
- k is the number of events we are interested in
In this case, we want to find P(X=5), which represents the probability of exactly 5 students arriving late. Plugging in the values into the formula:
P(X=5) = (e^(-3) * 3^5) / 5!
Calculating this expression, we get:
P(X=5) ≈ 0.10082
Therefore, the probability of 5 students being late in the 8-9AM class is approximately 0.10082, or about 10.08%.