Based on a​ survey,

3838​%

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

1414

likely voters are randomly selected. Complete parts​ (a) through​ (c) below.

Question content area bottom

Part 1

a. What is the probability that exactly

1111

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

​(qequals=1minus−​p).

​P(x)equals=StartFraction 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 xn!(n−x)!x!•px•(1−p)n−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=1414

Part 3

xequals=1111

Part 4

pequals=0.380.38

​(Type an integer or a decimal. Do not​ round.)

Part 5

Use these values to calculate

​P(1111​).

​P(1111​)equals=0.002070.00207

​(Round to five decimal places as​ needed.)

Part 6

b. If

1111

of the selected voters would do internet​ voting, is

1111

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 equals≤0.05.

Part 7

Use technology to calculate

​P(1111

or​ more).

​P(1111

or​ more) = 0.002420.00242

​(Round to five decimal places as​ needed.)

Part 8

Is this probability less than or equal to​ 0.05?

Yes

Your answer is correct.

No

Part 9

Use this information to determine whether

1111

voters willing to vote by internet is significantly high.

Part 10

c. Find the probability that at least one of the selected likely voters would do internet voting.

Use technology to calculate​ P(1 or​ more).

​P(1 or​ more) = enter your response here

​(Round to three decimal places as​ needed.)