A First Course in Probability (10th Edition)
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ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Transcribed Image Text:**Calculating Critical Value for Confidence Interval**
To calculate the critical value \( z_c \) necessary to form a confidence interval at the specified level of confidence, follow the steps outlined below.
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**Problem Statement:**
Find the critical value \( z_c \) necessary to form a confidence interval at the level of confidence shown below:
- \( c = 0.96 \)
**Calculation:**
\( z_c = \underline{\hspace{3cm}} \)
*Note: Please round your answer to two decimal places if necessary.*
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**Explanation:**
The critical value \( z_c \) can be found using the standard normal distribution table or a statistical calculator that provides the critical z-value for a given confidence level. The confidence level \( c \) denotes the probability that the true parameter lies within the confidence interval. For this problem, \( c = 0.96 \), which means we want to find the z-value where the area under the standard normal curve is 0.96.
Use the z-table to find the z-score corresponding to an area of \( \frac{1 + c}{2} \), which would be \( \frac{1 + 0.96}{2} = 0.98 \). Once you locate 0.98 in the z-table, the z-value corresponding to that area is the critical value \( z_c \).
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