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 (qequals1minusp). 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 xequals0, 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
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