07 Computing Normal Probabilities in Minitab
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07 Computing Normal Probabilities in Minitab


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.

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