Question

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-b < z < b) = 0.8516, find b. (i was trying to find it using invnorm on ti-84 because my teacher told us to. ive tried this question over 20 times i just dont know how to answer it. ive checked ultiple homework help sites pls help)

Answer 1

Normal Distributions

Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values (Investopedia, 2023).

Another relevant value is k, which represents the upper boundary of an interval.

Now, imagine P(-b < z < b) = 0.8516 on a normal distribution curve, with z at 0. The area under the curve between -b and b is 0.8516.

In terms of this curve, the k value would be b, with the interval being 0.8516 + whatever is to the left of this.

Let's determine k.

• 0.8516 ÷ 2 = 0.4258

(Let's imagine our normal distribution curve again. 0.4258 is the area between 0 and b.)

Now, add 0.4258 + 0.5 to determine the area to the left of k.

• 0.4258 + 0.5 = 0.9258

What we have now is this:

• P(x < k) = 0.9258
• k = invnorm(0.9258, 0, 1)
• k = 1.445

Since k = b, b = 1.445.

Answer

b = 1.445