A marine biologist would like to estimate the mean weight of all redfish on the Treasure Coast, using a $95 \%$ confidence interval. The standard deviation of the weights of all redfish on the Treasure coast is known to be 7.6 pounds. How large a sample of redfish should the marine biologist select so that the estimate is within 0.98 pounds of the true population mean. Round the solution up to the nearest whole number.
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Step 1 ：The problem is asking for the sample size needed to estimate the mean weight of all redfish on the Treasure Coast with a certain level of precision. The precision required is 0.98 pounds, and we know the standard deviation of the weights of all redfish is 7.6 pounds. We also know that we want a 95% confidence interval.

Step 2 ：The formula for the sample size in this case is given by: \(n = \left(\frac{Z_{\alpha/2} \cdot \sigma}{E}\right)^2\) where: \(Z_{\alpha/2}\) is the z-score corresponding to the desired confidence level (for a 95% confidence level, \(Z_{\alpha/2} = 1.96\)), \(\sigma\) is the standard deviation of the population (7.6 pounds in this case), \(E\) is the desired precision (0.98 pounds in this case).

Step 3 ：We can plug in the given values into this formula to find the required sample size. Since we can't have a fraction of a sample, we'll round up to the nearest whole number as the question instructs.

Step 4 ：The calculation returns a sample size of 232. This means that the marine biologist should select a sample of 232 redfish in order to estimate the mean weight within 0.98 pounds of the true population mean with a 95% confidence level. This result makes sense given the problem context.

Step 5 ：Final Answer: The marine biologist should select a sample of \(\boxed{232}\) redfish.