5.3.14-T Question Help A rare form of malignant tumor children. occurs in 11 chi

Question

5.3.14-T Question Help A rare form of malignant tumor children. 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 13,520 a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 13,520 children. b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 13,520 children is O 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? The mean number of cases is Tex (Type an integer or decimal rounded to three decimal places as needed.)

Explanation / Answer

Solution:

a) mean number of cases in groups of 13,520 children = np = 13520*0.000011 = 0.14872

b)here for poisson distribution ? = 0.14872

hence probability that the number of tumor cases in a group of 13,520 children is 0 =P(X=0)=e-? ?x/x! = 0.86181

probability that the number of tumor cases in a group of 13,520 children is 1 =P(X=1)=e-? ?x/x! = 0.12816

c) probability of more than one? case = P(X >1)=1-P(X<=1) =1-P(X=0)-P(X=1) = 1-0.86181-0.12816 = 0.01003

d) No as probabilty of more then one is less then 0.05; hence probability of cluster of four cases will also be less then 0.05 level which seems to be an unusual event

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