You are a campaign manager assigned to a fairly conservative rural dis

Adela Brown

Adela Brown

Answered question

2021-12-07

You are a campaign manager assigned to a fairly conservative rural district, where 65.3% of registered voters are in the Republican party. You hire a new pollster to gather some opinion data. In her report, she indicated that she interviewed twenty-six randomly selected voters, all of whom were Republican. What is the probability that all of the interviewees were Republican? Would you believe her? Why or why not?

Answer & Explanation

Carl Swisher

Carl Swisher

Beginner2021-12-08Added 28 answers

Step 1
Given,
n=26,
p=0.653
Find P(X=26)
We use binomial distribution formula to calculate this probability.
Step 2
Probability of exactly 26 is P(X=26):
=26C60.65326(10.653)0
=26!26!0!0.653260.3470
=0.00001540787
The probability is less than 0.05, which is unusual. So, we would not believe her.

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