Find the indicated mean.
-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 74,090,000 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 74,090,000 children).
A) 27,400
B) 274
C) 2740
D) 0.000037

Question

Quizplus · Accepted Answer

The mean of a Poisson distribution is equal to the expected number of occurrences in a given interval. Here, we need to find the mean number of cases of the disease in groups of 74,090,000 children.

The expected number of cases in a group of 74,090,000 children is the product of the probability of the disease occurring in a single child (0.000037) and the number of children in the group (74,090,000):
Expected number of cases = 0.000037 * 74,090,000 = 2.7433

Therefore, the mean of the Poisson distribution is 2.7433, which is closest to answer choice C (2740).

Find the Indicated Mean