Final answer:
The probability that the total number of errors in 12 essays is 5, with errors per essay following a Poisson distribution with mean t, can be calculated using the Poisson probability formula. The mean for 12 essays would be 12t, and the exact probability requires the value of t.
Step-by-step explanation:
The question is about finding the probability that the total number of errors in 12 randomly selected essays is 5, given that the number of errors per essay follows a Poisson distribution with mean t.
To calculate this probability, we need to consider the Poisson distribution for the total number of errors across all 12 essays, which would have a mean of 12t. The formula for the Poisson probability is:
P(X = x) = (e-λ λx) / x!
Where λ is the average rate (mean) of occurrences, x is the actual number of occurrences, and e is the base of the natural logarithm, approximately equal to 2.71828. Plugging the values into this formula, where λ = 12t and x = 5, we can find the desired probability p.
Without the actual value of t, we cannot compute the exact numeric probability.