Question: New research papers on COVID-19 are being produced every 2.5 minutes, on average (approximately as this is now a bit outdated, but you can see this article in Science).

1. (5 points) If this is true, what kind of distribution could model the current number of minutes per new research paper?
2. What would be the variance of this distribution?
3. Say we find the average number of minutes per paper by clocking the number of minutes between the next 82 papers and obtain a sample mean of 2.2 minutes between new papers. What do we know about the sampling distribution of the sample mean and how do we know this?
4. Give a 98% confidence interval about the population mean.
5. In a sentence or two, state what the 98% confidence interval from (e) tells us.
6. Suppose that we do not know the population standard deviation and, instead, the sample standard deviation is s = 2.8. What is the confidence interval about the population mean using the sample standard deviation? Compare this to your answer in part (e).

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