The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 54%. What is the probability that in a random sample of 450 voters, less than 48.3% say they will vote for the incumbent

0.0076 = 0.76% probability that less than 48.3% say they will vote for the incumbent.

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 54%. Sample of 450 voters.

This means that

What is the probability that in a random sample of 450 voters, less than 48.3% say they will vote for the incumbent?

This is the p-value of Z when X = 0.483. So

By the Central Limit Theorem

has a p-value of 0.0076

0.0076 = 0.76% probability that less than 48.3% say they will vote for the incumbent.

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step-by-step explanation:

step-by-step explanation:

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