Question

A rare form of malignant tumor occurs in 11 children in a​ million, so its probability is 0.000011. Four cases of this tumor occurred in a certain​ town, which had 15,359 children.

a. Assuming that this tumor occurs as​ usual, find the mean number of cases in groups of 15,359 children.

b. Using the unrounded mean from part ​(a​) ,find the probability that the number of tumor cases in a group of 15,359 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

(A) Mean number of cases= n*p

where n is the sample size = 15359 and p is probability = 0.000011

So, mean number of cases = 15359*0.000011 = 0.168949

(B) We have to find the probability of 0 or 1

Using the poisson distribution formula

setting the x= 0 and 1 and = 0.168949

(C) We know that total probability is always equal to 1

So,

we have already calculated in part(B) that

So,

(D) No, it is clear that probability of more than one case is 0.01276, which is very small and the probability of getting 4 cases will be smaller than 0.01276. Thus, we can say that cluster of four cases will not be a random chance, but a very unsual chance.