A biologist needs to estimate the weight of all slipper lobsters on the Treasure Coast. To achieve this, the biologist collects a random sample of 20 slipper lobsters. The weights of each lobster in the sample are given below. Assume that the weights of all slipper lobsters on the Treasure Coast are normally distributed. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline 2.1 & 5.1 & 4.5 & 5.4 & 3.7 & 2.3 & 3.1 & 5.3 & 3.4 & 4.5 \\ \hline 5.2 & 5.6 & 2.4 & 4.5 & 4.3 & 4.7 & 4.7 & 2.4 & 2.4 & 4.4 \\ \hline \end{tabular} Determine the point estimate, $\bar{x}$ and the sample standard deviation, $s$. Round the solutions to four decimal places, if necessary. \[ \begin{array}{l} \bar{x}=\square \\ s=\square \end{array} \] Using a $95 \%$ confidence level, determine the margin of error, $E$, and a confidence interval for the average weight of a slipper lobster on the Treasure Coast. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary. The margin of error is given by $E=$ A $95 \%$ confidence interval is given by

Step 1 ：Given the weights of 20 slipper lobsters, we are asked to find the point estimate, sample standard deviation, margin of error, and a 95% confidence interval for the average weight of a slipper lobster on the Treasure Coast.

Step 2 ：The weights of the lobsters are: 2.1, 5.1, 4.5, 5.4, 3.7, 2.3, 3.1, 5.3, 3.4, 4.5, 5.2, 5.6, 2.4, 4.5, 4.3, 4.7, 4.7, 2.4, 2.4, 4.4.

Step 3 ：The point estimate, denoted as \(\bar{x}\), is the sample mean. We calculate this by adding up all the weights and dividing by the number of lobsters. The point estimate is approximately 4.0000.

Step 4 ：The sample standard deviation, denoted as \(s\), is a measure of the amount of variation or dispersion of the weights. The sample standard deviation is approximately 1.1761.

Step 5 ：The margin of error, denoted as \(E\), is calculated using the z-score for a 95% confidence level, the standard deviation, and the square root of the sample size. The margin of error is approximately 0.52.

Step 6 ：The 95% confidence interval is calculated by subtracting and adding the margin of error from the point estimate. The 95% confidence interval for the average weight of a slipper lobster on the Treasure Coast is approximately (3.48, 4.52).

Step 7 ：So, the point estimate, \(\bar{x}\), is approximately 4.0000. The sample standard deviation, \(s\), is approximately 1.1761. The margin of error, \(E\), is approximately 0.52. The 95% confidence interval for the average weight of a slipper lobster on the Treasure Coast is approximately (3.48, 4.52).