Using the Binomial distribution. If n=9 and p=0.2, find P(x=6). A poll is given, showing 70% are in favor of a new building project. If 9 people are chosen at random, what is the probability that exactly 1 of them favor the new building project? A manufacturing machine has a 4% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect? About 5% of the population has a particular genetic mutation. 500 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 500. About 10% of the population has a particular genetic mutation. 700 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 700. About 8% of the population has a particular genetic mutation. 400 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 400. About 5% of the population has a particular genetic mutation. 900 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 900. Assume that a procedure yields a binomial distribution with a trial repeated \( n = 5 \) times. Use some form of technology to find the probability distribution given the probability \( p = 0.378 \) of success on a single trial.(Report answers accurate to 4 decimal places.)| \( k \) | \( P(X = k) \) ||--------|----------------|| 0 | || 1 | || 2 | || 3 | || 4 | || 5 | |This table is used to report the probabilities \( P(X = k) \) for various values of \( k \), where \( k \) represents the number of successes in \( n = 5 \) trials. Each row corresponds to the probability of achieving exactly \( k \) successes out of the five trials. The values should be calculated using a binomial probability formula or relevant statistical software and reported to four decimal places. ### Cumulative Probability Distribution Calculation**Scenario:**Assume that the proportion of voters who prefer Candidate A is \( p = 0.162 \). Organization D conducts a poll of \( n = 5 \) voters.Let \( X \) represent the number of voters polled who prefer Candidate A. Use some form of appropriate technology (e.g., your calculator or statistics software like Excel, R, or StatDisk) to find the cumulative probability distribution.**Instructions:**(Report answers accurate to 4 decimal places.)**Cumulative Probability Distribution Table:**| \( k \) | \( P(X \leq k) \) ||--------|------------------|| 0 | || 1 | || 2 | || 3 | || 4 | || 5 | |To complete the table, follow these steps:1. **Define the parameters:** - The number of trials, \( n = 5 \) - The probability of success (voter prefers Candidate A), \( p = 0.162 \)2. **Cumulative probability distribution:** - Use the binomial cumulative distribution formula or statistical software functions to calculate the cumulative probabilities for \( k = 0, 1, 2, 3, 4, 5 \).3. **Software/Calculator Usage:** - In Excel, use the function \(\text{BINOM.DIST}(k, n, p, TRUE)\) for cumulative probabilities. - In R, use the function \(\text{pbinom}(k, n, p)\). - In StatDisk, input the values in the Binomial Distribution Calculator.By calculating these values, you will fill in the table accurately with the cumulative probabilities for each value of \( k \).

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Answered: Using the Binomial distribution. If n=9…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

Related questions

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A poll is given, showing 70% are in favor of a new building project. If 9 people are chosen at random, what is the probability that exactly 1 of them favor the new building project?

A manufacturing machine has a 4% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect?

About 5% of the population has a particular genetic mutation. 500 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 500.

About 10% of the population has a particular genetic mutation. 700 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 700.

About 8% of the population has a particular genetic mutation. 400 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 400.

About 5% of the population has a particular genetic mutation. 900 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 900.