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Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, $x$, for the sample size provided.
Lower bound $=0.334$, upper bound $=0.736, n=1000$

The point estimate of the population proportion is $\square$.
(Round to the nearest thousandth as needed.)
The margin of error is $\square$.
(Round to the nearest thousandth as needed.)
The number of individuals in the sample with the specified characteristic is $\square$.
(Round to the nearest integer as needed.)

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Final Answer: The point estimate of the population proportion is \(\boxed{0.535}\). The margin of error is \(\boxed{0.201}\). The number of individuals in the sample with the specified characteristic is \(\boxed{535}\).

Steps

Step 1 :Given the lower bound of the confidence interval is 0.334 and the upper bound is 0.736, and the sample size is 1000.

Step 2 :The point estimate of the population proportion is the midpoint of the confidence interval, which can be calculated as the average of the lower and upper bounds. So, \(\frac{0.334 + 0.736}{2} = 0.535\).

Step 3 :The margin of error is the difference between the point estimate and either the lower or upper bound of the confidence interval. So, \(0.736 - 0.535 = 0.201\) or \(0.535 - 0.334 = 0.201\).

Step 4 :The number of individuals in the sample with the specified characteristic can be calculated by multiplying the point estimate by the sample size. So, \(0.535 \times 1000 = 535\).

Step 5 :Final Answer: The point estimate of the population proportion is \(\boxed{0.535}\). The margin of error is \(\boxed{0.201}\). The number of individuals in the sample with the specified characteristic is \(\boxed{535}\).

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