Math Problem Statement

Based on a​ survey, 34​% of likely voters would be willing to vote by internet instead of the​ in-person traditional method of voting. For each of the​ following, assume that 13 likely voters are randomly selected. Complete parts​ (a) through​ (c) below. Question content area bottom Part 1 a. What is the probability that exactly 10 of those selected would do internet​ voting? In a binomial probability​ distribution, probabilities can be calculated by using​ technology, a table of binomial​ probabilities, or the binomial probability​ formula, shown below where n is the number of​ trials, x is the number of successes among n​ trials, p is the probability of success in any one​ trial, and q is the probability of failure in any one trial ​(qequals1minus​p). ​P(x)equalsStartFraction n exclamation mark Over left parenthesis n minus x right parenthesis exclamation mark x exclamation mark EndFraction times p Superscript x Baseline times left parenthesis 1 minus p right parenthesis Superscript n minus x ​, for xequals​0, ​1, 2,​ ..., n While either technology or the binomial probability formula can be used to find the simple binomial​ probabilities, for this​ exercise, use technology. Part 2 First find the values of​ n, x, and p. nequals    13 Part 3 xequals    10 Part 4 pequals    0.34 ​(Type an integer or a decimal. Do not​ round.) Part 5 Use these values to calculate ​P(10​). ​P(10​)equals select: 0.00143 0.00170 ​(Round to five decimal places as​ needed.) Part 6 b. If 10 of the selected voters would do internet​ voting, is 10 significantly​ high? Why or why​ not? Having x successes among n trials is a significantly high number of successes if the probability of x or more successes is 0.05 or less. That​ is, x is a significantly high number of successes if​ P(x or ​more)less than or equals0.05. Part 7 Use technology to calculate ​P(10 or​ more). ​P(10 or​ more) =    enter your response here ​(Round to five decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Probability Theory

Formulas

P(x) = (n! / ((n-x)!x!)) * p^x * (1-p)^(n-x)
P(x or more) = P(x) + P(x+1) + ... + P(n)

Theorems

Binomial Probability Theorem

Suitable Grade Level

Grades 10-12