Pulse Rates. In Exercises 13–24, use the data in the table bel...

Question

Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.

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For males, find P90 which is the pulse rate separating the bottom 90% from the top 10%.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In a study on the weight distribution of adult male cats, the weights are normally distributed with a mean of 10 pounds and a standard deviation of 1.2 pounds. What is the weight that separates the lowest 97.5% from the highest 2.5% of this population? Awesome. So it appears for this particular prompt, we're asked to ultimately solve for what is the weight that separates the lowest 97.5% from the highest 2.5% of this specific male cat population. Awesome. So now that we know that we're ultimately trying to solve for the weight that separates the lowest from the highest of the specific population, let's read off our multiple choice answers to see what our final answer might be, noting that they're all in the same units of pounds. So A is 11.250, B is 7.648. C is 12.352 and D is 8.875. Awesome. So, first off, in order to solve for this particular prompt, we need to find the Z score that corresponds to our population P, which, as we should note that our population P for this particular case is equal to 0.975, which we took our percentage and we divided it by 100 to write it as a decimal. So that's how we got our P equals 0.975. So now we need to recall and use the standard normal distribution table, and when we do that, we will find that Z or Z score is going to be equal to 1.96. And once again, you can use your standard normal distribution table, which should be provided in your textbook. So moving right along here, our next step now is we need to substitute the values into our Z score formula, and as we should recall, the Z score formula states that Z to Z score is equal to X. Minus mu divided by sigma, where sigma denotes the standard deviation, mu denotes the mean, and capital X is the value that we are interested in. So, in this case, we need to note, let's make a note here that Z is going to be equal to 1.96. Meal or mean is gonna be equal to 10 pounds. And our sigma, our standard deviation values equal to 1.2 pounds. So that means when we plug in all of our known variables, we will get 1.96 is equal to X minus our value for the mean, which is 10 pounds divided by 1.2 pounds. So now what we need to do is we need to rearrange this equation to isolate and solve for X, because that is our unknown value. So I'm gonna skip a few steps, but ultimately, if you use a little bit of algebra to get X all by itself, you will find that X is going to be equal to 12.352, and that's when we round to three decimal places, and don't forget that it's units of measurement are in pounds. So LB. So to make sure. That we don't get confused, I'll use a little curly L so we know that it's pounds and not like 1 B. Awesome, so that's it. That is how we solve for this particular problem. Hooray, we did it. So therefore, the weight that separates the bottom 97.5% from the top 2.5% is 12.352 pounds, and this corresponds to multiple choice answer, letter C, which is 12.352 pounds. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Pulse Rates. In Exercises 13–24, use the data in the table below for pulse rates of adult males and females (based on Data Set 1 “Body Data” in Appendix B). Hint: Draw a graph in each case.

For males, find P90 which is the pulse rate separating the bottom 90% from the top 10%.

Key Concepts

Percentiles

Normal Distribution

Standard Deviation

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