Refer to the accompanying data display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of \( 95 \% \) was used. Complete parts (a) and (b) below. \[ \begin{array}{l} \quad \text { TInterval } \\ (85.74,91.76) \\ \bar{x}=88.75 \\ S x=8.897431411 \\ n=36 \end{array} \] a. Express the confidence interval in the format that uses the "less than" symbol. Round the confidence interval limits given that the original times are all rounded to one decir \[ 85.74 \mathrm{~min}<\mu<9176 \mathrm{~min} \] (Round to two decimal places as needed.) b. Identify the best point estimate of \( \mu \) and the margin of error. The point estimate of \( \mu \) is \( \square \) minutes. (Round to two decimal places as needed.)
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The confidence interval for the mean time between eruptions of the Old Faithful geyser is established between 85.74 minutes and 91.76 minutes. So you can express this as: \( 85.74 \, \text{min} < \mu < 91.76 \, \text{min} \). For part b, the best point estimate of \( \mu \) is the sample mean \(\bar{x} = 88.75\) minutes. The margin of error is calculated as half the width of the confidence interval. So, it is the difference between the upper limit (\(91.76\)) and the point estimate, which is \( 91.76 - 88.75 = 3.01 \) minutes. Thus, the point estimate of \( \mu \) is \( 88.75 \) minutes and the margin of error is \( 3.01 \) minutes.
