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# Leakage from underground fuel tanks has been a source of ISBN: 9780073401331 38

## Solution for problem 7SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Problem 7SE

Leakage from underground fuel tanks has been a source of water pollution. In a random sample of 87 gasoline stations, 13 were found to have at least one leaking underground tank.

a. Find a 95% confidence interval for the proportion of gasoline stations with at least one leaking underground tank.

b. How many stations must be sampled so that a 95% confidence interval specifies the proportion to within ±0.03?

Step-by-Step Solution:

Step 1 of 2:

(a)

In this question, we are asked to find a 95% confidence interval for the proportion of gasoline stations with at least one leaking underground tank.

In a random sample of 87 gasoline stations, 13 were found to have at least one leaking underground tank.

Let be the number of success in independent Bernoulli trials with success probability , so that .

Define and Then a level confidence interval for p (proportion) is ………..(1)

Let represent the gasoline stations with at least one leaking underground tank.

The number of successes is , and the number of trials is , then we can say follows the Binomial distribution.

We therefore compute, , =  For a 95% confidence interval, the value of is,   and Then for is , hence The 95% confidence interval is therefore from equation (1),  (0.0886, 0.241)

Hence 95% confidence interval is (0.0886, 0.241).

Step 2 of 2

##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 7SE from 5 chapter was answered, more than 257 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 7SE from chapter: 5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: stations, underground, proportion, tank, confidence. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “Leakage from underground fuel tanks has been a source of water pollution. In a random sample of 87 gasoline stations, 13 were found to have at least one leaking underground tank.a. Find a 95% confidence interval for the proportion of gasoline stations with at least one leaking underground tank.________________b. How many stations must be sampled so that a 95% confidence interval specifies the proportion to within ±0.03?” is broken down into a number of easy to follow steps, and 67 words.

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