Use standard normal distribution to find P(-2.25<z<0)

Answer 1

Hey David,

Hope you are doing well. Happy to help!

A standard normal distribution as you know has mean 0 and standard deviation 1. We convert any normal distribution to a standard normal distribution by calculating what's called a z score through the following formula:

z = (x - mean) / (standard deviation)

In this case, we want to find the probability that a given z score is between -2.25 and 0. However, a normal distribution is a continuous distribution, so we really need to find the area between z = -2.25 and z = 0.

Notice that the standard normal distribution is symmetric at z = 0 and because all probabilities add to 1, the area under the entire standard normal distribution is 1. Therefore, to find P(-2.25 <= z <= 0), we can approach as such:

P(-2.25 <= z <= 0) = P(z <= 0) - P(z <= -2.25). We know that P(z <= 0) = 0.5 because symmetry at z = 0.

P(z <= -2.25) = 0.0122 (search up a normal distribution probability table in Google Images!)

0.5 - 0.0122 ~ 0.4878. Hope this helps!