A certain rare form of cancer occurs in 37 children in a million, so its probability is 0.000037. In the city of Normalville there are 74,090 children. A Poisson distribution will be used to approximate the probability that the number of cases of the disease in Normalville children is
More than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases
In groups of 74,090 children).
A) 27,400
B) 2.7
C) 274
D) 0.000037

Question

Quizplus · Accepted Answer

The mean ($\lambda$) of a Poisson distribution is given by the expected number of occurrences, which can be calculated by multiplying the probability of an event by the number of trials. Here, the probability of a child having this rare form of cancer is 0.000037, and there are 74,090 children in Normalville. Thus, the mean is $0.000037 \times 74,090 = 2.74133$, which rounds to approximately 2.7.

A Certain Rare Form of Cancer Occurs in 37 Children