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Step 1:I'll solve this step-by-step using the standard normal distribution approach:
Step 2:: Understand the Confidence Interval
For a confidence interval, we need to find the z-score that corresponds to the given confidence level. In this case, we have a 98% confidence interval.
Step 3:: Calculate the Area in Each Tail
A 98% confidence interval means that the total area in both tails is $$1 - 0.98 = 0.02$$.
This means each tail will have 0.02 \div 2 = 0.01 area.
Step 4:: Find the z-score
To find the z-score, we need to look up the z-value that leaves 0.01 in each tail of the standard normal distribution.
Step 5:: Use the Standard Normal Distribution Table
This means the critical z-values are $$-2.33$$ and $$+2.33$$.
Final Answer
Note: This value ensures that 98% of the data falls within the interval, with 1% in each tail of the distribution.
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