When would use normalcdf or normalpdf?

Are you referring to probability or z-score calculations regarding normalcdf and normalpdf?

could you elaborate on both?

CDF is continuous density function and PDF is probability community function.

Think of CDF as cumulative probability as it starts with a C.

Think of PDF as a point probability as it starts with a P

If the problem asks what is the probability that x=y use PDF.

If the problem asks what is the probability that x>y or x<y use CDF.

If you are talking about z-scores… here’s a problem that demonstrates how you could use both:

Let’s say that data has been collected to find the typical weight of pugs. The data shows that the mean weight of a pug is 18 pounds, with a standard deviation of 2 pounds.

If you want to find the probability that a pug weighs less than 16 pounds… you would use CDF. You could use normalcdf(lower bound, upper bound, mean, standard deviation) = normalcdf(-1000, 16, 18, 2) = .159. So about 16% of pugs weigh less than 16 pounds. (Think of this one telling you what percent of the data falls within a range).

Note: I used -1000 as an extreme lower bound because we want anything lower than 16.

If you wanted to find out if a value is extreme (find its z-score), you would use PDF. So let’s say we want to find how extreme it is to have a pug who weighs 22 pounds… normpdf(statistic, mean, standard deviation) = normalpdf(22, 18, 2) = .027 So we can say that only 2.7% of pugs weight more than 22 pounds (think of this one telling you what percentile you’re at).