Suppose that a fast food restaurant decides to survey its customers to gauge interest in a breakfast menu. After surveying multiple people, the restaurant created a 95% confidence interval for the proportion of customers interested in a breakfast menu. The confidence interval is (0.688,0.766) . Use the confidence interval to find the point estimate and margin of error for the proportion. Give your answer precise to three decimal places.

point of estimate for the proportion of customers interested in a breakfast menu

represent the margin of error.

Step-by-step explanation:

For this case we want to find a confidence interval for the proportion of customers interested in a breakfast menu.

The confidence interval for this case is given by this formula:

And the margin of error is given by:

The 95% confidence for this case is given by:

We can find the point of estimate for the proportion using the fact that the interval is symmetrical

And we can find the margin of error with this difference:

Or equivalently with:

So then the final answer for this case would be:

point of estimate for the proportion of customers interested in a breakfast menu

represent the margin of error.