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 ????
0.2534
0.1008 using the poisson distribution
To find the probability, we need to make an assumption about the distribution of student lateness. Let's assume that the number of students who arrive late follows a Poisson distribution with a mean of 3.
In a Poisson distribution, the probability of a given number of events occurring in a fixed interval is proportional to the mean of the distribution. The formula for the probability of observing exactly k events in a Poisson distribution is:
P(k) = (e^(-λ) * λ^k) / k!
Where:
- P(k) is the probability of observing exactly k events
- e is the mathematical constant approximately equal to 2.71828
- λ is the average number of events (mean)
In this case, the average number of students arriving late (mean) is 3. We want to find the probability of 5 students being late (k = 5). Plugging these values into the formula, we get:
P(5) = (e^(-3) * 3^5) / 5!
Calculating this gives us the probability that exactly 5 students will be late in the 8-9AM class.