Clinic took temperature readings of 250 flu patients OveT = Weckend and discovered the lemperalure distribution lo be Gaussian; with mean of I0I.90 "F and st...

Human body temperatures for healthy individuals have approximately a normal distribution with mean $98.25^{\circ} \mathrm{F}$ and standard deviation. $75^{\circ} \mathrm{F} .$ The past accepted value of $98.6^{\circ} \mathrm{F}$ was obtained by converting the Celsius value of $37^{\circ},$ which is correct to the nearest integer.)
(a) Find the 90th percentile of the distribution.
(b) Find the 5 th percentile of the distribution.
(c) What temperature separates the coolest 25$\%$ from the others?

Behold this glorious, normal bell shaped curve right there in the middle is going to be our average new one. Standard deviation now from it is going to be in red, which is going to have 68% of all of our data, We go on another standard deviation two. Standard deviations away from the mean and that's going to have 95% of our data. This is where the 5% of unusualness comes from. If something is 5% chance of not happening or happening is considered to be unusual. And outside of those two standard deviations, As for the third standard deviation, that's going to have 99.5 of all of our data. So, our first question asked, Yeah, What is the approximate percentage of healthy adults with body temperatures that are within one standard deviation of the mean? Or between 97.58 and 98.82, why don't we put those bounds there? And Red 97 58 And 98.82. Yeah. So we are also given that the mean is 98.2°F. Yeah. And a standard deviation of 062. Mhm Yeah, Yeah. So now we can get to finally answering your question and for one standard deviation this is going to allow for 68% of our data. Yeah. And then for part B between 96.34 and 100.06°F. Now this seems a little high for the 100.6, considering that we can only go up by increments of .62. So I'm gonna guess that that's going to be three standard deviations away. So what we can do to verify this is take her average which is 98.2 and add that to three times are standard deviation, So that's gonna be three times 0.62 mm. And what we end up getting is exactly 100.06. Mhm. Mhm. And I made a small mistake on copying are 99.5 was supposed to be 99.7, so this is going to encompass 99.7% of the graph when we go from 96.34°F and 100.06.

We're going to answer question number 28 in your textbook body temperatures based on the sample data and data set three in appendix b assume that human body temperatures are normally distributed with a mean of 98.2 degrees and a standard deviation of 0.62. So, in our staff called application, you can see here, I have a mean of 98.2 and a standard deviation of 0.62. Bellevue Hospital in new york city uses 100.6 degrees. Fahrenheit is the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggested a cut off of 100.6 is appropriate. So we're looking for The value to the right of 100.6. Mhm You can see that's very very small. Um The area is only .01%. So it's all the way up here actually, 100.6 is right there. So very small percentage Party says physicians want to select a minimum temperature for requiring further medical test. What should that temperature be? If we want only 5% of healthy people to exceed it. So we want to calculate a value To the left of .5. Um and that should be 97.1, I'm sorry, I want to do to the right of .05. Uh so that should be 99.22. That should be the minimum temperature uh for 5% of healthy people to exceed

So we're gonna be applying Chevy Chef serum to the temperatures. Uh since it's a bell shaped distribution were allowed to do this um And let's get started. So the mean is going to be 98.2. Yeah, and that's going to be in degrees Fahrenheit. Some people put it right up there And our sigma are standard deviation is going to be 0.62. Our Chevy Chevy five Theorem application will be to find out how much of our data is going to be within three standard deviations of the mean. So that's gonna be one minus one of our case square where K is the number of standard deviations we have. So that's one And this 1/3 squared. So we're gonna have 1 -1/9 or 8/9 Which is equal to a percentage of 89%. And then we can find out the upper and lower bounds simply by taking our average of 98.2 mhm Adding and subtracting the three standard deviations of 062 mm. Yeah. To get our upper and lower bounds, so for our lower This is going to be equal to 96.34 degrees Fahrenheit. And for upper bounds This is going to be 106 degrees Fahrenheit

The final solution for number 28 a nurse thinks that the temperature for surgical patients is above the normal 98.2 degrees Fahrenheit. And so it asks us what the hypotheses are. So the knoll always has to have some sort of equality. So the knowledge that The main new population mean is equal to 98.2. And then the alternative, she's thinking that it's above. So that means me was greater than 98.2. And it gives you a mini tab. Print out. The P value is just labeled as the P The P Values .23 given to you. And then it also says what's the conclusion? I don't know if I made no, I didn't. But the conclusion um would be there is not enough evidence to suggest. Um The mean temp of all her surgical Sure. If I spelled that wrong, surgical patients is above 98.2°F.