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 16,560 children.

a. Assuming that this tumor occurs, as usual, find the mean number of cases in groups of 16,650 children.

b.Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 16,560 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 exactly 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.)

d.Let a probability of 0.05 or less be "very small," and let a probability of 0.95 or more be "very large". Does the cluster of our cases appear to be attributable to random chance? Why or why not?

A.Yes, because the probability of more than one case is very small.

B.No, because the probability of more than one case is very large.

C.Yes, because the probability of more than one case is very large.

D.No, because the probability of more than one case is very small.

Answer 1

Que.a

Let, X = Number of children having malignant tumor.

n = sample size = 16560

p = Probability of occurring malignant tumor = 0.000011

X follows Binomial distribution with parameter n and p.

Mean number of cases= n*p = 16560 * 0.000011 = 0.182

Que.b

Since n is very large and p is very small Binomial distribution is well approximated by Poisson distribution with parameter

Pmf of Poisson distribution is,

Thus,

Que.c

Que.d

Yes, because the probability of more than one case is very small.