![]() ![]() ![]() Now, we just need to learn how to read the probabilities off of each of the tables. ![]() That is, for \(Z\)-values, to two decimal places, between 0.00 and 3.49, we can use Table Vb to find probabilities such as \(P(Z>0.12), P(Z>1.96)\), and \(P(Z>3.32)\). Here's what the top of Table Vb looks like: Table Vb: The Normal Distribution -3 -2 -1 0 1 2 3 0.1 0.2 0.3 0.4 α z α z f(z) Table Vb, on the other hand, gives probabilities in the upper tail of the standard normal distribution. So, let's find the cumulative distribution function \(F(z)\), which is also incidentally referred to as \(\Phi(z)\) in the standard normal case (that's the greek letter phi, read "fee"): We need to show that the random variable \(Z\) follows a \(N(0,1)\) distribution. What is the Z table formula for the normal distribution Z (X ) / where X is a normal random variable, is the mean of X, and is the standard deviation of X. Follows the \(N(0,1)\) distribution, which is called the standardized (or standard) normal distribution. ![]()
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