Final answer:
To find the critical value z a/2 for an 85% confidence level, you need to find the z-score that leaves 0.925 of the probability to its left in a standard normal distribution. Using tables or a calculator function like invNorm, the z a/2 critical value is approximately 1.445.
Step-by-step explanation:
The student is asking to find the critical value z a/2 that corresponds to the confidence level of 85%. The confidence level represents the percentage of the time that a statistical result would be correct if you repeated the experiment multiple times. The formula for confidence interval involves this critical value z a/2, among other variables, to account for the level of certainty we have in a sample statistic.
To find the critical value z a/2, we look at the standard normal distribution where the confidence level of 85% or 0.85 is in the middle, and the alpha (α) level is 1 - CL which in this case is 1 - 0.85 = 0.15. This alpha is split into two tails, each with an area of 0.075. The critical value z a/2 corresponds to the z-score that has a 0.925 area to the left of it (as the left tail cuts off 0.075). Using standard normal distribution tables or calculator functions like invNorm(1 - α/2, 0, 1) can yield this critical value.
Searching standard normal probability tables or using calculator functions for 0.925, we find the critical value z a/2 to be approximately 1.445. However, if you are using statistical software or a calculator, you might directly find this critical value by looking up the invNorm function with a cumulative area of 0.925.