Question

Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 156 eligible voters aged​ 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged​ 18-24, 22% of them voted.

The probability that fewer than 37 voted

Answer 1

The following information has been provided about the population proportiona and the sample size:

Population Proportion =	0.22
Sample Size =	156

We need to compute. Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Observe that:

which indicates that the assumption for normal approximation for the sampling distribution is met.

Since we need to use a continuity correction, we need to use the factor

to adjust the end points of the end points of the probability intervals, so the new limits are:

Now, the following is obtained using normal approximation:

Therefore, based on the information provided, it is concluded that

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