A rare form of malignant tumor occurs in 11 children in a million, so its probab

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 17 comma 259 children. a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 17 comma 259 children. b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 17 comma 259 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?

Explanation / Answer

a) mean number of cases in groups of 17259 children =np =17259*0.000011=0.189849~ 0.19

probability that the number of tumor cases in a group of 17259 children is 0 or 1 =P(X<=1)=P(X=0)+P(X=1)

=e-0.19*0.190/0!+e-0.19*0.191/1! =0.8271+0.1570 =0.9841

b)

probability of more than one case =P(X>1) =1-P(X<=1) =1-0.9841 =0.0159

c) probability of 4 or more cases =P(X>=4) =1-P(X<=3) =0.00005

as probability of happening that is very less ; therefore it is not  attributable to random chance.

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