The exponential probability distribution can be used to model waiting time in line or the lifetime of

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The exponential probability distribution can be used to model waiting time in line or the lifetime of electronic components. Its density function is skewed right. Suppose the wait-time in a line can be modeled by the exponential distribution with \(\mu=\sigma=5\) minutes.

(a) Simulate obtaining a random sample of 15 wait-times.

(b) Explain why constructing a \(95 \%\) confidence interval using Student's \(t\)-distribution is a bad idea. Nonetheless, construct a  \(95 \%\) confidence interval using Student's \(t\)-distribution.

(c) Use the data to construct a \(95 \%\) confidence interval for the mean using 1000 resamples.

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