Question

Question Help 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 19,195 children. a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 19,195 children. b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 19, 195 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? a. The mean number of cases is (Type an integer or decimal rounded to three decimal places as needed.) b. The probability that the number of cases is exacty 0 or 1 is Round to three decimal places as needed.) c. The probability of more than one case is Round to three decimal places as needed.) Click to select your answer(s).

Answer 1

P(malignant tumor) = 0.000011

a) Mean number of cases in a group of 19,195 children = 19,195 x 0.000011

= 0.211

b) P(number of tumor cases is 0 or 1) = (1 - 0.000011)¹⁹¹⁹⁵ + 19194x0.000011x(1 - 0.000011)¹⁹¹⁹⁴

= 0.8097 + 0.1709

= 0.981

c) P(more than 1 case) = 1 - P(0 or 1 case)

= 1 - 0.981

= 0.019

d) B. No, because the probability of more than one case is very small