Problem

.1-9.3) Question 3 of 10 This question: $1 \mathrm{p}$ $K$ Compute the critical value $z_{\alpha / 2}$ that corresponds to a $85 \%$ level of confidence. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). \[ z_{\alpha / 2}=\square \] (Round to two decimal places as needed.)

Solution

Step 1 :The level of confidence is 85%, which means the level of significance, $\alpha$, is 1 - 0.85 = 0.15.

Step 2 :Since we are looking for $z_{\alpha / 2}$, we need to divide $\alpha$ by 2, which gives us 0.075.

Step 3 :We then look for this value in the standard normal distribution table to find the corresponding z-score.

Step 4 :The critical value $z_{\alpha / 2}$ that corresponds to a $85 \%$ level of confidence is approximately 1.44 when rounded to two decimal places.

Step 5 :Final Answer: $z_{\alpha / 2} = \boxed{1.44}$

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