**Example Problem: Tumor Probability Analysis**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 14,224 children.**Questions:****a.** Assuming that this tumor occurs as usual, find the mean number of cases in groups of 14,224 children.**b.** Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 14,224 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?**Solution Approach:**1. **Mean Number of Cases (Part a):** - To find the mean number of cases, multiply the probability of one case by the number of children. 2. **Probability Calculation (Part b and c):** - Use the Poisson distribution to determine the probabilities of having 0, 1, or more than one case based on the mean number of cases. 3. **Analysis of Cluster (Part d):** - Compare the observed cases to the expected distribution to infer if the cluster is likely due to random chance.

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Description: **Example Problem: Tumor Probability Analysis**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 14,224 children.**Questions:****a.** Ass

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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 14,224 children. a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 14,224 children. b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 14,224 children is 0 or 1. c. What is the probability of more than one case?

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 14,224 children. a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 14,224 children. b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 14,224 children is 0 or 1. c. What is the probability of more than one case?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

**Example Problem: Tumor Probability Analysis**

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 14,224 children.

**Questions:**

**a.** Assuming that this tumor occurs as usual, find the mean number of cases in groups of 14,224 children.

**b.** Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 14,224 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?

**Solution Approach:**

1. **Mean Number of Cases (Part a):**
- To find the mean number of cases, multiply the probability of one case by the number of children.

2. **Probability Calculation (Part b and c):**
- Use the Poisson distribution to determine the probabilities of having 0, 1, or more than one case based on the mean number of cases.

3. **Analysis of Cluster (Part d):**
- Compare the observed cases to the expected distribution to infer if the cluster is likely due to random chance.

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