Refer to Example 1. How large a sample of wind turbines is needed to ensure that, with at least \(95 \%\) confidence, the error in our estimate of the sample proportion is at most 0.06 if

(a) nothing is known about the population proportion?

(b) the population proportion is known not to exceed 0.20 ?

Data From Example 1

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EXAMPLE I Point estimate of a binomial proportion p An engineering firm responsible for maintaining and improving the performance of thousands of wind turbines is asked to check on the sound levels. The purpose is to determine the proportion that currently would not meet proposed new sound level restrictions. A random selection of n = 55 wind turbines reveals that 8 operate too loudly according to the proposed new restrictions. Obtain a point estimate of the proportion of their wind turbines that do not meet specifications.