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Find the critical value $z_{\alpha/2}$ that corresponds to the given confidence level. $\newline$ $99$ % $\newline$ $z_{\alpha/2}=\square$ (Round to two decimal places as needed.).

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Find values of normal variables

Full solution

Q. Find the critical value

z_{\alpha/2}

that corresponds to the given confidence level.

\newline

99

%

\newline

z_{\alpha/2}=\square

(Round to two decimal places as needed.).

Determine Confidence Level: To find the critical value $z_{\alpha/2}$ for a $99\%$ confidence level, we need to determine the z-score that corresponds to the tail areas in a standard normal distribution. Since the confidence level is $99\%$ , the area in the tails ( $\alpha$ ) is $1 - 0.99 = 0.01$ . This area is split equally between the two tails, so each tail has an area of $0.01 / 2 = 0.005$ .
Calculate Tail Areas: We need to find the z-score that has $0.005$ to its right in the standard normal distribution. This is typically done using a z-table or statistical software. For a z-table, we look for the closest probability to $0.005$ in the table, which will give us the corresponding z-score.
Find Z-Score: Upon looking at the z-table, we find that the z-score that corresponds to an area of $0.005$ to the right is approximately $2.576$ . This means that $z_{\alpha/2}$ is approximately $2.576$ .
Round Critical Value: We are asked to round the critical value to two decimal places. The value we found is already at two decimal places, so no further rounding is necessary.

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