Final answer:
To get a 90 percent confidence interval, we must include the central 90 percent of the probability of the normal distribution. The interval of z values that has a 90% chance of containing z is approximately -1.645 to 1.645.
Step-by-step explanation:
To get a 90 percent confidence interval, we must include the central 90 percent of the probability of the normal distribution. If we include the central 90 percent, we leave out a total of a = 10 percent in both tails, or 5 percent in each tail, of the normal distribution.
The critical value 1.645 is the z-score in a standard normal probability distribution that puts an area of 0.90 in the center, an area of 0.05 in the far left tail, and an area of 0.05 in the far right tail. To capture the central 90 percent, we must go out 1.645 standard deviations on either side of the calculated sample mean. The critical value will change depending on the confidence level of the interval.
The interval of z values that has a 90% chance of containing z is approximately -1.645 to 1.645.