Computing normal probabilities in Minitab. Whether your distribution is modeled

with the normal distribution, given a mean and a standard

deviation, or you have already computed a Z score, you can use Minitab

to look up a probability. You can go to calc, probability distributions, normal. {silence} In an introductory statistics class, we will not

use the first option in Minitab, probability density, instead, we’ll be looking up an less than or equal to

probability. Minitab calls this cumulative probability. And if we’re

given the probability in advance and we want to reverse the process and

look up the value of X or a Z, we’ll use the inverse cumulative probability option. Let’s say that we’re looking at a normal

distribution with a mean of two and a standard deviation of one.

We would like to find the probability that X is less than or equal to four. In Minitab, this is a cumulative probability.

Once we have selected this, which is the default, we can then enter the mean

and standard deviation. In our example the mean is two and the standard deviation is one. Since we’re computing just one probability, the probability that X is less than

or equal to four, we’ll select input constant and enter four. {silence} When we click ok, Minitab will tell us the cumulative probability.

That’s right here. {silence} Now let’s reverse the process. Let’s say the

probability was given to us. Let’s say the cumulative probability is 0.50. We want to find the value of X that is at

the fiftieth percentile. We will go back to calc, percentile, probability distributions, normal. {silence} Since we are reversing the process, we want an inverse cumulative probability. The mean is still two and the standard deviation

is one. So, I do not have to change that part. But for the input constant we will enter that cumulative probability that was

already given to us, 0.50. Please do not enter a fraction into this area.

Use the decimal format. {silence} When we click ok, Minitab first tells us the cumulative probability that we asked for. Then it tells us the value of two. That’s the answer that

we’re looking for. This is a little different than the output for the binomial and

poisson distributions. {silence} Let’s say you already converted your normal

distribution into a Z score or the standard

normal distribution. We can use the same operation in Minitab to

compute the probability.

We’ll go back to calc, probability distributions, normal. Let’s say we computed a Z score of negative three and we want to know

the probability that Z is less than that value. That’s a

cumulative probability. The mean and standard deviation need to be changed to fit the

standard normal distribution. The mean is zero and standard deviation is one. {silence} If we want the probability that Z is less than or

equal to negative three, negative three is the input constant. {silence} When we hit ok, Minitab will give us the cumulative probability. Let’s reverse the process. Let’s say for the standard

normal distribution, we want to know the value of Z that is at the .975 percentile. We’ll go back to calc, probability distributions, normal. We are reversing the process. That’s called an inverse cumulative probability. For the standard normal distribution, Z, the mean is zero and standard deviation is one. The input constant is that probability that’s

given to us, the 0.975. When we click ok, Minitab will give us the value of Z. First, Minitab tells us the probability that we asked for. Next, it tells the actual value of Z. Usually we round this up to 1.96.

## 4 Comments

## barbaric37

Thanks for all the great instructional videos!

## Aly Louisa

Thank you! This helped me with my minitab assignment. ðŸ™‚

## Jason Janson

Thanks for showing me how to do the standard normal distribution. It'll be nice to get away from using the cumulative probability tables.

## garpertw

Thank you, it helped me to do what i wanted