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Elden [556K]
3 years ago
10

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n=500, x=

200, 95% confidence
Mathematics
1 answer:
DiKsa [7]3 years ago
5 0

Answer:

0.3581<x<0.4429

Step-by-step explanation:

Using the formula for calculating the confidence interval of the population proportion p expressed as:

Confidence interval = p ± Z * √p(1-p)/n

p is the population proportion = x/n

p = 200/500

p = 0.4

Z is the z-score at 95% CI = 1.96

n is the sample size = 500

Substituting the given parameters into the formula we will have;

Confidence interval = 0.4 ± 1.96 * √p(1-p)/n

Confidence interval = 0.4 ± 1.96 * √0.4(0.6)/500

Confidence interval = 0.4 ± 1.96 * √0.24/500

Confidence interval = 0.4 ± 1.96 * √0.00048

Confidence interval = 0.4 ± 1.96 * 0.0219

Confidence interval = 0.4±0.04294

Confidence interval = (0.3571, 0.4429)

Hence the confidence interval of the population mean is 0.3581<x<0.4429

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The distance that he has traveled exists 73km 500m.

<h3>What is the distance?</h3>

Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.

Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.

To estimate the distance that he has traveled

He covered 7/8 out of 84 km

So, 7/8 × 84 = 73.5 km

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Therefore, the distance that he has traveled exists 73km 500m.

To learn more about distance refer to:

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Answer: 11 is the required number that always divides such differences for the following types of numbers.

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