A poll reported 42% of voters favor the Republican candidate in an upcoming election. Assume that this percentage is true for the current population of all registered voters. Calculate the probability that less than 45% of a sample of 40 voters will vote for the Republican candidate. (Hint: you need to consider this as a sampling distribution).

64.80% probability that less than 45% of a sample of 40 voters will vote for the Republican candidate.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Considering a proportion p in a sample of size n as a sampling distribution, we have that

In this problem, we have that:

So

Calculate the probability that less than 45% of a sample of 40 voters will vote for the Republican candidate.

This is the pvalue of Z when X = 0.45. So

has a pvalue of 0.6480

64.80% probability that less than 45% of a sample of 40 voters will vote for the Republican candidate.

step-by-step explanation:

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