Question

In: Statistics and Probability

A study determines that 60% of the voters in a town intend to vote for the...

A study determines that 60% of the voters in a town intend to vote for the incumbent mayor. if a sample of 8 people is selected, approximate probability that 6 of the 8 people surveyed intend to vote for the incumbent is

Expert Solution

Solution :

Let X be a random variable which represents that out of 8 people the number of people who voted for the incumbent mayor.

Given that, 60% of voters in a town intend to vote for the incumbent mayor.

Hence, probability that a voter will vote for this incumbent mayor is 0.60.

Let's consider "a voter who vote for incumbent mayor" as success. Hence, we have only two mutually exclusive outcomes (success and failure) for each of the trials.

Probability of success (p) = 0.60

Number of trials (n) = 8

Since, probability of success remains constant in each of the trials, number of trials is finite and outcomes are independent, therefore we can consider that X follows binomial probability distribution with parameters n = 8 and p = 0.60.

According to binomial probability law, probability of occurrence of exactly x successes in n trials is given by

Where, p is probability of success.

We have to find P(X = 6).

We have, p = 0.60 and n = 8

Using binomial probability law we get,

Hence, the probability that 6 of the 8 people surveyed intend to vote for the incumbent is 0.2090.

Please rate the answer. Thank you.

orchestra answered 1 year ago

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