Question

a rare form of malignant tumors occurs in 11 children in a Million ,so it's probability is 0.000011.
4 cases of this tumor occurred in a certain town which had 19673 children.
a) assuming that the rumor occurs as usual find the mean number of cases in a group of 19673 ?
b) using the unrounded mean from part A find the probability that the number of cases in group of 19673 children is 0 or 1?
c) what is the probability of more than one case?
d) does the cluster of four cases appear to be attributable to random chance why or why not?

Answer 1

The number of tumors in 19673 children can be modeled by Poisson distribution.

The Poisson PMF is

a) For 19673 children, the mean (the Poisson parameter)

b) The probability that the number of cases in group of 19673 children is 0 or 1

c) The required probability is

d) We can see that

Hence, the cluster of four cases appears to be attributable to random chance.

Yes.