The average height of the US male is approximately 68 inches. What is the probability of selecting a group of males with average height of 72 inches or greater with a standard deviation of 5 inches?

Hey everyone. So let's take a look at this practice question. Here it says the average height of the US male is approximately 68 inches What is the probability of selecting a group of males with average height of 72 inches or greater with a standard deviation of 5 inches. So I know we were talking about confidence intervals, but realize that confidence intervals can be linked to the idea of probability. If we can 0 in on our probability for a selected group, that in the extension can be our confidence in our findings. So here what we're going to do to answer this question to find the probability, we're going to have to first figure out what our z value is. Remember, your z value equals your value, which we'll say is x minus your Mean. In this case, since we're dealing with the population, it'll be our population Mean, which is divided by our Standard Deviation. And here, if we're dealing with our population standard deviation, we're gonna do it here as our Sigma. And so what we're gonna do here from our information, we said that our value is 72 inches and then minus our mean or average, which is 68, divided by our standard deviation, which is 5. So So when I plug that in that's going to give me 0.800. Now remember with probability we use our z table here and if we're take a look here we're looking at the probability. Remember here this represents our meaner average of our population. Our probability is what's residing within this location in terms of our graph, and we're dealing with 0.800 for our z value. So remember the first two digits come from this column here so we're dealing with 0.8 and it's 0.800 so our last digits comes from this section here, our last digit. If we're to line these up it falls at 0.7881. So that represents our probability. So probability which is p equals 0.7881. To change it into its percentage form, we multiply by 100. So that gives me 78.81%. So that's the probability of selecting a group of males that are 72 inches or greater when we have this 5 inch standard deviation. So that's my probability and with it I have confidence in my ability to figure out and find that percentage of males within this selected group. So again, we could talk about probability and how it's closely connected to our idea idea of confidence intervals.