find z score using standard normal table

If the population data set has a mean of 10 and a standard deviation of 5 then the probability from 10 to 15, one standard deviation, is the same as from zero to 1, one standard deviation on the standard normal distribution. However, the essential point here is, the probability for one standard deviation on one normal distribution is the same on every normal distribution. But only if our data has a mean of zero and a standard deviation of 1. The table has solved our integral calculus problem. At the top of the table is the shaded area in the distribution which is the probability for one standard deviation. That number, 0.3413 is the probability from zero to 1 standard deviation.

Using the standard normal table, typically called the normal table, to find the probability of one standard deviation, go to the Z column, reading down to 1.0 and then read at column 0. The Standard Normal has a random variable called Z. The solution is to convert the distribution we have with its mean and standard deviation to this new Standard Normal Distribution.

The only problem is that even with this table, it would be a ridiculous coincidence that our data had a mean of zero and a standard deviation of one. The shaded area in the graph at the top of the table in Statistical Tables represents the probability from zero to the specific Z value noted on the horizontal axis, Z. The table in this text is the most common presentation and is set up with probabilities for one-half the distribution beginning with zero, the mean, and moving outward. These have been produced and are available here in the appendix to the text or everywhere on the web. We can now quite easily calculate all probabilities for any value of x, for this particular normal distribution, that has a mean of zero and a standard deviation of 1.

Putting these values into the formula it reduces to a very simple equation. This particular normal distribution is given the name Standard Normal Distribution.

But now, remembering that there are an infinite number of normal distributions out there, we can consider the one with a mean of zero and a standard deviation of 1. The integral of the normal probability density function between the two points x 1 and x 2 is the area under the curve between these two points and is the probability between these two points.ĭoing these integrals is no fun and can be very time consuming. The mathematical tool needed to find the area under a curve is integral calculus. This shows that the area between X 1 and X 2 is the probability as stated in the formula: P (X 1 ≤ x ≤ X 2)

Find z score using standard normal table