Andy W. answered • 03/27/21
Academic Tutor Specializing in Math Subjects
Because we know that the random variable has a standard normal distribution, the mean will be 0 and standard deviation will be 1. So we simply have to read the Z table to find the answer.
In case you don't know how to read the Z table, you read the leftmost column first. Then you read the uppermost column. All this is done to find the probability for a certain Z score. For example, to find the probability for Z < 1.96, you look at the left column for 1.9, then you look for the top row for 0.06. See where the values meet and you get 0.9750 as the probability. This is the probability that represents the left side of the Z score.
For P(Z > 1.32) (it doesn't matter whether this is greater than or equal to or not because normal distribution is a continuous distribution, meaning that the random variable can also include decimals), you pretty much go through the same thing as I did in the example above. By doing that, you find a value of 0.9066. However, what you found represents P(Z < 1.32) because that's only the left side. Because we're finding greater than, you would take the complement, which would be the opposite of what we found. This would be 1 - 0.9066 = 0.0934.
