Questions: Find the critical value (zc) necessary to form a confidence interval at the level of confidence shown below. (c=0.97) (zc=) (Round to two decimal places as needed.)

Find the critical value (zc) necessary to form a confidence interval at the level of confidence shown below. (c=0.97) (zc=) (Round to two decimal places as needed.)
Transcript text: Find the critical value $z_{c}$ necessary to form a confidence interval at the level of confidence shown below. \[ c=0.97 \] \[ z_{c}= \] $\square$ (Round to two decimal places as needed.)
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Solution

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Find the critical value \( z_{c} \) for a confidence level of \( c = 0.97 \).

Step 1: Determine the tail area.

For a confidence level of \( c = 0.97 \), the area in the tails is \( 1 - c = 1 - 0.97 = 0.03 \). Since the normal distribution is symmetric, each tail will have an area of \( \frac{0.03}{2} = 0.015 \).

Step 2: Find the z-score corresponding to the tail area.

Using the standard normal distribution table or a calculator, find the z-score that corresponds to a cumulative probability of \( 1 - 0.015 = 0.985 \). This z-score is approximately \( 2.17 \).

Step 3: Round the z-score to two decimal places.

The z-score \( 2.17 \) is already rounded to two decimal places.

\\(\boxed{z_{c} = 2.17}\\)

\\(\boxed{z_{c} = 2.17}\\)

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