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A clinic took temperature readings ol 250 flu palients Over weekend and discovered the temperature distribution t0 be Gaussian, with mean ol [01.90 aIU standard dev...

Question

A clinic took temperature readings ol 250 flu palients Over weekend and discovered the temperature distribution t0 be Gaussian, with mean ol [01.90 aIU standard deviation of 0,5460) Use this normal error curve area lable to caleulate each value. What the Traction ol palients expecled to havc fever ereuler than (2,49fraction above 102.99What the fruction palients expexledMMi"etempxralure hetween [01.79 JllI 102,28 "Tractic belween [0.79 {l 1(2,28

A clinic took temperature readings ol 250 flu palients Over weekend and discovered the temperature distribution t0 be Gaussian, with mean ol [01.90 aIU standard deviation of 0,5460) Use this normal error curve area lable to caleulate each value. What the Traction ol palients expecled to havc fever ereuler than (2,49 fraction above 102.99 What the fruction palients expexled MMi"e tempxralure hetween [01.79 JllI 102,28 " Tractic belween [0.79 {l 1(2,28



Answers

Based on Data Set 3 in Appendix B, body temperatures of healthy adults have a bell­shaped distribution with a mean of 98.20 ° F and a standard deviation of 0.62 ° F . Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures a. within 1 standard deviation of the mean, or between 97.58 ° F and 98.82 ° F ? b. between 96.34 ° F and 100.06 ° F ?

Hands. Claris. When you right here. So we're giving her mean last 98.25 Fahrenheit and standard aviation this point fought 75 burning. So, the party, we're gonna find the 90% tall. So we have access people, too. I mean, plus C standard aviation. We spend a normal distribution table, but we work backwards. So for 99 0.21 does this 90th percentile source The volume is 1.22 for our fifth percentile. We know that 5% it's gonna give us a value of C is equal to negative 1.6 pork. Why? So you get 97.2 and reports seen it separates the coolest. 25% says he calls negative 250.67 And since 0.2514 value is the table to the closest 2.25 So blink to 51 fork. We're gonna use our C formula see formula, which is a born too negative 0.67 Just legal to X minus. I needed 0.25 over 175 Get X is equal to 97.75

The following is a solution for number 17 and this is the mean temperature for humans. Uh saying that it's 98.6. And we're testing to see if it's actually less than 98.6. And we're giving some information here that X bar was 98.2 And s was .7 and the sample size was quite large of 700. So, um what we're gonna do here is find this is going to be a T. Test. So we're going to find the test statistic and I'm actually gonna find that with a calculator. So if we go to stat and then test and you can find those with a formula to But if we go to T test here, you can put your immune not that's your hypothesized value in the X bar, your standard deviation your sample size. And then just change that alternative to less than And then whenever you calculate, you get a test statistic of negative 15. Now this p value zero. So we'll come back to that here in a second. But The test statistic is negative 15 119. And we're doing the critical region method at least for this first part. So we need to find the critical region or the critical value T. Star will call it. So if we go to 2nd distribution and go to university, We're testing this at the point a one level of significance and degrees of freedom will be the sample size -1. So it's 699. And whenever we paste that is negative 2.33. So that's the critical value here. So negative 2.33. All right there. So anything to the left and negative 2.33. We reject. And this test statistic is heavily in the left, so we're going to reject H not. So the average is in fact less than uh 98.6 and then asked for the P value. It's essentially zero. So p value would be zero. And again, we would also reject H dot. So the mean temperature for humans is in fact less than 98.6 degrees Fahrenheit.

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


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