Question: In the movie "When Harry Met Sally", there is a scene where Meg Ryan is shopping for a Christmas tree. The film shows a beautiful snowy night in New York city and Meg Ryan dragging her tree back to her apartment. Suppose the mean height of a sample of \(\mathrm{n}=15\) Christmas trees was \(\overline{\mathrm{X}}=143 \mathrm{~cm}\). Assume that the population of tree heights is normal with known standard deviation \(\sigma=18 \mathrm{~cm}\)

1. Construct a \(90 \%\) confidence interval estimate of the unknown mean \(\mu\).
2. Have a look at the CI that you constructed in answering question #1a. On the basis of its lower bound, is it reasonable to say that the average tree height in the population is at least \(130 \mathrm{~cm}\) ? Explain.

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