# Use the Poisson distribution to find the indicated probabilitiesDisease Cluster Neuroblastoma, a rare form of malignant tumor, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children.a. Assuming that neuroblastoma occurs as usual, find the mean number of cases in groups of 12,429 children.b. Using the unrounded mean from part (a), find the probability that the number of neuroblastoma cases in a group of 12,429 children is 0 or 1.c. What is the probability of more than one case of neuroblastoma?d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?

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Use the Poisson distribution to find the indicated probabilities

Disease Cluster Neuroblastoma, a rare form of malignant tumor, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children.

a. Assuming that neuroblastoma occurs as usual, find the mean number of cases in groups of 12,429 children.

b. Using the unrounded mean from part (a), find the probability that the number of neuroblastoma cases in a group of 12,429 children is 0 or 1.

c. What is the probability of more than one case of neuroblastoma?

d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?

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Step 1

a)

Mean of Poisson distribution:

The formula is given by,

Step 2

b)

Define the random variable x as the number of cases with neuroblastoma. Here, the numbers of cases are random and each case of neuroblastoma is independent from the other. Also, the occurrences (cases for neuroblastoma) are uniformly distributed. Then, x follows the Poisson distribution.

The Poisson distribution formula is,

Step 3

Thus, the probability for the number of neuroblastoma cases in the group of 12,42...

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