**Problem Statement:**1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines. - **Distribution Type:** ______________ - **Probability:** ______________**Explanation:**This problem involves determining the probability of the first success (audit required) on the 25th trial when there is a constant probability of success on each trial. The distribution type typically used for this kind of problem is the geometric distribution.To solve this:- Let $ p $ be the probability that a tax return requires an audit, $ p = \frac{1}{100} = 0.01 $.- The probability that the first audit happens on the 25th tax return is calculated using the formula for the geometric distribution: \[ P(X = k) = (1-p)^{k-1} \cdot p \] where $ k $ is the 25th trial.- By substituting the values, \[ P(X = 25) = (0.99)^{24} \cdot 0.01 \]- Calculate to find the probability.

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Description: **Problem Statement:**1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines. - **Distribution Type:** ______________ - **Probabili

we want find that the first audit is the 25th return the auditor examines which means that we want…

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1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines. Distribution type: Probability:

1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines. Distribution type: Probability:

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

**Problem Statement:**

1. One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that the first audit is the 25th tax return the auditor examines.

- **Distribution Type:** ______________
- **Probability:** ______________

**Explanation:**

This problem involves determining the probability of the first success (audit required) on the 25th trial when there is a constant probability of success on each trial. The distribution type typically used for this kind of problem is the geometric distribution.

To solve this:

- Let $ p $ be the probability that a tax return requires an audit, $ p = \frac{1}{100} = 0.01 $.
- The probability that the first audit happens on the 25th tax return is calculated using the formula for the geometric distribution:

\[
P(X = k) = (1-p)^{k-1} \cdot p
\]

where $ k $ is the 25th trial.

- By substituting the values,

\[
P(X = 25) = (0.99)^{24} \cdot 0.01
\]

- Calculate to find the probability.

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