A company wants to estimate, at a 95% confidence level, the proportion of all families who own its product. A preliminary sample showed that 30.0% of the families in this sample own this company's product. The sample size that would limit the margin of error to be within 0.047 of the population proportion is:

The sample size is of 366.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

The margin of error is of:

A preliminary sample showed that 30.0% of the families in this sample own this company's product.

This means that

95% confidence level

So , z is the value of Z that has a p-value of , so .

The sample size that would limit the margin of error to be within 0.047 of the population proportion is:

This is n for which . So

Rounding up:

The sample size is of 366.

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

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