A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this certain tumor occurred in a certain town, which had 12,696 children. a. Assuming that this tumor occurs, as usual, find the mean number of cases in groups of 12,696 children. b. Using the unrounded mean from part a, find the probability that the number of tumor cases in a group of 12,696 children is 0 or 1. c. What is the probability of more than one case?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this certain tumor occurred in a certain town, which had 12,696 children.

a. Assuming that this tumor occurs, as usual, find the mean number of cases in groups of 12,696 children.

b. Using the unrounded mean from part a, find the probability that the number of tumor cases in a group of 12,696 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 cause? Why or why not?

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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
13,924
children.
 
a. Assuming that this tumor occurs as​ usual, find the mean number of cases in groups of
13,924
children.
b. Using the unrounded mean from part
​(a​),
find the probability that the number of tumor cases in a group of
13,924
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?
 
 
 

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Part 1
a. The mean number of cases is
0.1530.153.
​(Type an integer or decimal rounded to three decimal places as​ needed.)
Part 2
b. The probability that the number of cases is exactly 0 or 1 is
0.9890.989.
​(Round to three decimal places as​ needed.)
Part 3
c. The probability of more than one case is
0.0110.011.
 ​(Round to three decimal places as​ needed.)
Part 4
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 four cases appear to be attributable to random​ chance? Why or why​ not?
 
 
A.
​No, because the probability of more than one case is very small.
 
B.
​Yes, because the probability of more than one case is very small.
 
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 large.
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