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A biologist examines 15 sedimentary samples for lead concentration. The mean lead concentration for the sample data is $0.511\mathrm{cc}/\mathrm{cubic}$ meter with a standard deviation of 0.0598 . Determine the $98\mathrm{\%}$ confidence interval for the population mean lead concentration. Assume the population is approximately normal.

Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

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Step 1 ：A biologist examines 15 sedimentary samples for lead concentration. The mean lead concentration for the sample data is $0.511\mathrm{cc}/\mathrm{cubic}$ meter with a standard deviation of 0.0598. We are asked to determine the $98\mathrm{\%}$ confidence interval for the population mean lead concentration, assuming the population is approximately normal.

Step 2 ：The first step is to find the critical value that should be used in constructing the confidence interval. This is done by calculating the Z-score for a $98\mathrm{\%}$ confidence interval.

Step 3 ：The Z-score is calculated using the formula for the percentile of a normal distribution, which is given by the inverse of the cumulative distribution function. For a $98\mathrm{\%}$ confidence interval, we want the Z-score that corresponds to the $99\mathrm{\%}$ percentile, because the $98\mathrm{\%}$ confidence interval is the range between the $1\mathrm{\%}$ and $99\mathrm{\%}$ percentiles.

Step 4 ：Using the scipy.stats library in Python, the Z-score for the $99\mathrm{\%}$ percentile is calculated as follows: $\text{z\_score}=\text{stats.norm.ppf}(0.99)$.

Step 5 ：The calculated Z-score is approximately $2.326$.

Step 6 ：Final Answer: The critical value that should be used in constructing the $98\mathrm{\%}$ confidence interval is approximately $\boxed{{\displaystyle 2.326}}$.