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The level of confidence c is the area under the standard normal curve between the critical values minus−z Subscript czc and z Subscript czc. The area outside the critical values is 1minus−​c, so the area in each tail is one half left parenthesis 1 minus c right parenthesis
1
2(1−c). Use the standard normal distribution table or technology to find the critical value z Subscript czc.

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Answer:

To find the critical value \( z_{c} \) for a given level of confidence \( c \), we need to look up the area between the critical values in the standard normal distribution table or use technology.

Since the area in each tail is \( \frac{1 - c}{2} \), we can find the area to the left of the critical value, which is \( \frac{1 - c}{2} + c \). We then look up this area in the standard normal distribution table or use technology to find the corresponding \( z \)-score.

For example, if \( c = 0.95 \) (which corresponds to a 95% confidence level), then the area to the left of the critical value is \( \frac{1 - 0.95}{2} + 0.95 = 0.975 \). Looking up the \( z \)-score corresponding to an area of 0.975 in the standard normal distribution table or using technology, we find the critical value \( z_{c} \).

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