Here, the term scale means how far apart the scores are (their spread) and where they are located (their central tendency). \(z\)-ScoresĪnother convenient characteristic of \(z\)-scores is that they can be converted into any “scale” that we would like. If you have that resting heartbeat, then the school nurse is going to give you some additional screening.\): Standardized scores. 84.77 and they want us to round to the nearest whole number. And this will get us 0.53 times nine is equal to 4.77 plus 80 is equal to 84.77. So to get the value, we would take our mean and we would add 0.53 standard deviation. Well, this just means 0.53 standard deviations above the mean.
0.53, right over there, and we just now have to figure out what value gives us a z-score of 0.53. Get to the 67%, 68, 69, we're getting close and on our table this is the lowest z-score that gets us across that 70% threshold. When we look at this, and we are to the right of the mean, and so we're gonna haveĪ positive z-score. We want it to be at least 70% and then come up with theĬorresponding z-score. This time we're lookingįor the percentage. Started with the z-score and were looking for the percentage. The standard deviation to come up with an actual value. And then we can take that z-score and use the mean and So what we can do, we can use a z-table to say for what z-score is 70% of the distribution less than that. So that means that thisĪrea right over here is going to be 30% or 0.3. Let's say it is right over here, that if you are at that score, you have reached the minimum threshold to get an additional screening. And you could also go standardĭeviations below the mean, this right over here wouldīe 71, this would be 62, but what we're concernedĪbout is the top 30% because that is who is going to be tested. So on this normal distribution, we have one standardĭeviation above the mean, two standard deviations above the mean, so this distance right over here is nine. The standard deviation is nine beats per minute. And they tell us several things about this normal distribution. They're telling us that the distribution of resting pulse ratesĪre approximately normal. Know how to tackle this, I encourage you to pause this Receive additional screening? Round to the nearest whole number. Pulse rate at that school for students who will Whose resting pulse rates are in the top 30% of the To provide additional screening to students Mean of 80 beats per minute and standard deviation Of resting pulse rates of all students at Santa Maria High School was approximately normal with
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