http://www.ck12.org Chapter 5. Normal Distribution
Now find the probability for az−score of− 1 .58. It is often a good idea to estimate this value before using the table
when you are first getting started. Thisz−score is between−2 and−1. We know from the empirical rule that the
probability forz=−1 is approximately.16 and similarly, for−2 it is around.025, so we should expect to get a
value somewhere between these two estimates.
Locate the stem and the leaf for− 1 .58 on Table 5.5 and follow them across and down to the corresponding
probability. The answer appears to be approximately 0.0571, or approximately 5.7% of the data in a standard
normal curve is below az−score of− 1 .58.
It is extremely important, especially when you first start with these calculations, that you get in the habit of relating
it to the normal distribution by drawing a sketch of the situation. In this case, simply draw a sketch of a standard
normal curve with the appropriate region shaded and labeled.
Let’s try an example in which we want to find the probability of choosing a value that isgreater thanz=− 0 .528.
Before even using the table, draw a sketch and estimate the probability. Thisz−score is just below the mean, so the
answer should be more than 0.5. Thez−score of− 0 .5 would be half way between 0 and−1, but because there is
more area concentrated around the mean, we could guess that there should be more than half of the 34% of the area
in this section. If we were to guess about 20−25%, we would estimate an answer of between 0.70 and 0.75.