P(z < -1.5 or z > 2.50) =

With "or", it is unclear whether you want the probability between the scores, above them or below them.

Assuming that you want the probability between the Z scores, find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the Z scores.

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To calculate the probability P(z < -1.5 or z > 2.50), we can break it down into two separate probabilities and then add them together.

First, let's find the probability of z < -1.5.

The standard normal distribution (also known as the Z-distribution) has a mean of 0 and a standard deviation of 1. We need to find the area to the left of -1.5 on the Z-distribution curve. We can use a Z-table or a calculator to look up the corresponding probability.

Using a Z-table, we find that the probability of z < -1.5 is approximately 0.0668.

Next, let's find the probability of z > 2.50.

Again, using a Z-table or a calculator, we look up the area to the left of 2.50 on the Z-distribution curve. However, since we need the probability of z > 2.50, we subtract this probability from 1 to get the area to the right.

Using a Z-table, we find that the probability of z > 2.50 is approximately 1 - 0.9938 = 0.0062.

Now, we can add the two probabilities together:

P(z < -1.5 or z > 2.50) = P(z < -1.5) + P(z > 2.50)
= 0.0668 + 0.0062
= 0.073

Therefore, P(z < -1.5 or z > 2.50) is approximately 0.073.