THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
-In a box of 16 chocolates,there are four chocolates with coconut filling.What is the probability of choosing four chocolates,none of which have coconut fillings?
A)0.272
B)0.264
C)0.248
D)0.236

Question

Quizplus · Accepted Answer

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known average rate.The probability of choosing four chocolates, none of which have coconut fillings, is given by the following formula:P(X = 0) = (e^-λ * λ^x) / x!where:λ is the average number of successes in a given intervalx is the number of successesIn this case, λ = 4.2 and x = 4.Plugging these values into the formula, we get:P(X = 0) = (e^-4.2 * 4.2^4) / 4! = 0.272Therefore, the probability of choosing four chocolates, none of which have coconut fillings, is 0.272.