yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Finding z-score for a percentile | AP Statistics | Khan Academy


3m read
·Nov 11, 2024

The distribution of resting pulse rates of all students at Santa Maria High School was approximately normal, with a mean of 80 beats per minute and a standard deviation of nine beats per minute. The school nurse plans to provide additional screening to students whose resting pulse rates are in the top 30% of the students who are tested.

What is the minimum resting pulse rate at that school for students who will receive additional screening? Round to the nearest whole number. If you feel like you know how to tackle this, I encourage you to pause this video and try to work it out.

All right, now let's work this out together. They're telling us that the distribution of resting pulse rates is approximately normal, so we could use a normal distribution. They tell us several things about this normal distribution: they tell us that the mean is 80 beats per minute, so that is the mean right over there.

They tell us that the standard deviation is 9 beats per minute. So on this normal distribution, we have one standard deviation above the mean, two standard deviations above the mean. So this distance right over here is N9. So this would be 89. This one right over here would be 98.

You could also go standard deviations below the mean. This right over here would be 71. This would be 62. But what we're concerned about is the top 30% because that is who is going to be tested.

So there's going to be some value here, some threshold, let's say it is right over here, that if you are at that score, you have reached the minimum threshold to get additional screening; you are in the top 30%. So that means that this area right over here is going to be 30% or 0.3.

What we can do is use a z-table to say for what z-score is 70% of the distribution less than that. Then we can take that z-score and use the mean and the standard deviation to come up with an actual value.

In previous examples, we started with the z-score and were looking for the percentage. This time, we're looking for the percentage; we want it to be at least 70% and then come up with the corresponding z-score.

So let's see. Immediately when we look at this, we are to the right of the mean, and so we're going to have a positive z-score. We're starting at 50% here; we definitely want to get this 67%, 68%, 69%. We're getting close and on our table, this is the lowest z-score that gets us across that 70% threshold. It's at 0.719, so definitely crosses the threshold.

And so that is a z-score of 0.53. 0.52 is too little, so we need a z-score of 0.53. Let's write that down, 0.53 right over there. Now we just have to figure out what value gives us a z-score of 0.53.

Well, this just means 0.53 standard deviations above the mean. So to get the value, we would take our mean and we would add 0.53 standard deviations. So 0.53 times 9 will get us.

0.53 * 9 is equal to 4.77. Plus 80 is equal to 84.77. They want us to round to the nearest whole number, so we will just round to 85 beats per minute.

So that's the threshold. If you have that resting heartbeat, then the school nurse is going to give you some additional screening; you are in the top 30% of students who are tested.

More Articles

View All
Geometric random variables introduction | Random variables | AP Statistics | Khan Academy
So, I have two different random variables here, and what I want to do is think about what type of random variables they are. So, this first random variable X is equal to the number of sixes after 12 rolls of a fair die. Well, this looks pretty much like …
Safari Live - Day 372 | National Geographic
Program features live coverage of an African safari and may include animal kills and carcasses. Viewer discretion is advised. Well, good afternoon everybody and welcome to a spectacular start to the afternoon safari with one of our leopards we don’t see …
How Hidden Technology Transformed Bowling
A portion of this video was sponsored by Salesforce. This is the biggest, most in-depth video about bowling ever. How bowling balls are made, the best way to throw them, maximize strikes, how the lanes are oiled, what it takes to be a pro, and how this sp…
Electric current | Physics | Khan Academy
Electricity that lights up a bulb looks very different than lightning strikes, but they’re actually more similar than one might think because they both have electric current. So, let’s understand what electric current is, how they are produced, and also g…
The Gray Rock Method | Beat ‘Toxic People’ with Serenity
Some people really get in our hair. Moreover, there are individuals that, for some reason, take delight in getting emotional reactions out of others. When they succeed, they win, and their ability to hurt gives them a sense of power. Whether we call them …
Hiroki Takeuchi
Now on to the next speaker this afternoon. Heroi is a co-founder and CEO of Go Cardless, which is the UK’s leading direct debit provider. They now serve more businesses than any other direct debit provider, and they’re also expanding to serve Europe. Hero…