reading a table for standard normal distribution z scores

These are the same results we found above using the table,Īlthough these have more significant digits. We could approach this as just finding the sum In this case we want to use the fact that Here we will just run through an example of each, butĪn example of the first problem might be to find P(X 0.97).įigure 6 displays the portion of the same table Using symmetry and the earlier information we have assigned probabilities to the various regions inĪpproaches to solving all of these were presented on the (A better value would be 0.954499876, but we will just use 0.95 for now.) 2 and 2 accounts for about 95% of the total area (1 square unit) If we move out another standard deviation, we find that the region between Quite a bit of knowledge from just one graph! This symmetry means that P(X 1) ≈ 0.16, or Since the probability that a random variable,Ĭurve and to the left of the vertical line at that value, Normal distribution is a symmetric distribution. Looking back at Figure 1 (or at Figure 1a if you like) No longer gives that impression of a 'bell' shape. This figure is no more or less accurate inĭisplaying the normal curve, but Figure 1a

If we had equal scales the curve would appearĪs in Figure 1a. We magnify the y scale by stretching it so that the vertical spread In Figure 1 we go from -4 to 4 on the x scale, but To point out that part of the visual effect of the curve depends upon The 'can be made to look somewhat like' is added We will learn, later, how to change values from a non-standard normal distribution We refer to the values along the traditional x-axis as z values The normal distribution is often called a bell-shaped curveįor the obvious reason that the graph of the function can beĪ careful 'read' of the graph in Figure 1 reveals that we are calling values along the traditional That is, the curve isĪlways above the x-axis even for values more extreme than -4 or 4. We must note here that the curve never gets to the x-axis.

It takes 40 such areas to equal 1 square unit. Each small rectangle in Figure 1 representsĠ.5*0.05 or 0.025 square units.

Remember that as a probability density function, the area under the curveĪnd above the axis is equal to 1 square unit. With those values the general formula becomesĪ graph of that function appears in Figure 1. With such a definition we get a different valueįor each different combination of μ and σ.įortunately, we can look at a single example, called the standard normal distribution, Where we are given values for the mean, μ, The normal distribution is defined by a mathematical formula,

Listing of all R commands used on this page.The Expanded Notation for pnorm() and qnorm().Normalizing a non-standard normal distribution.Probability: Normal Distribution Probability: Normal Distribution

Reading a table for standard normal distribution z scores