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Find the critical value
z_(C) necessary to form a confidence interval at the level of confidence shown below.

c=0.80

Find the critical value $z_{C}$ necessary to form a confidence interval at the level of confidence shown below. $\newline$ $c=0.80$

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Solve quadratic inequalities

Full solution

Q. Find the critical value

z_{C}

necessary to form a confidence interval at the level of confidence shown below.

\newline

c=0.80

Understand concept critical value: Understand the concept of a critical value in the context of a confidence interval. The critical value $z_{C}$ is the z-score that corresponds to the desired level of confidence. It is the value that captures the central area under the standard normal distribution curve. For a confidence level of $0.80$ , we want to find the z-score that leaves $10\%$ in each tail (since $100\% - 80\% = 20\%$ , and this is split between the two tails of the distribution).
Use distribution table: Use a standard normal distribution table or calculator to find the z-score that corresponds to an area of $0.90$ to the left of it. $\newline$ Since we want to leave $10\%$ in the upper tail, we look for the z-score that has $90\%$ of the distribution to its left ( $0.80$ for the middle plus $0.10$ for the lower tail).
Find z-score: Find the z-score from the standard normal distribution table or calculator. $\newline$ Using a z-table or calculator, we find that the z-score that corresponds to an area of $0.90$ to the left is approximately $1.28$ .

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