Question

find the critical value ( z_{alpha/2} ) that corresponds to the confidence level 86%.( z_{alpha/2} = square )(round to two decimal places as needed.)

Explanation:

Step1: Calculate alpha value

$\alpha = 1 - 0.86 = 0.14$

Step2: Find $\alpha/2$

$\frac{\alpha}{2} = \frac{0.14}{2} = 0.07$

Step3: Find cumulative area

Cumulative area = $1 - 0.07 = 0.93$

Step4: Look up z-score for 0.93

Using a standard normal table or calculator, the z-score corresponding to a cumulative area of 0.93 is approximately 1.48.

Answer:

1.48