z Scores. In Exercises 5–8, express all z scores with two deci...

Question

z Scores. In Exercises 5–8, express all z scores with two decimal places.

Diastolic Blood Pressure of Females For the diastolic blood pressure measurements of females listed in Data Set 1 “Body Data” in Appendix B, the highest measurement is 98 mm Hg. The 147 diastolic blood pressure measurements of females have a mean of 70.2 mm Hg and a standard deviation of 11.2 mm Hg.

b. How many standard deviations is that [the difference found in part (a)]?

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. For the total cholesterol levels in units of milligrams per deciliter. Of adults, the highest recorded measurement is 240 mg per deciliter. The 180 recorded cholesterol levels have a mean of 195 mg per deciliter, and a standard deviation of 30 mg per deciliter. Determine the Z score for the highest recorded cholesterol level. Using the mean and standard deviation of the recorded levels. Awesome. So it appears for this particular problem we're ultimately trying to solve for the Z score value using our mean and standard deviation. So we're trying to determine the Z score for the highest recorded cholesterol level, using our mean and standard deviation, and that is our final answer we're ultimately trying to solve for. Awesome. So now that we know what we're trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is 5.63, B is 4.72, C is 2.35, and D is 1.67. Awesome. So first off, in order to solve this problem, let's take a moment to write down all of our known variables, all the variables that are given to us by the problem itself. So we're told that the highest recorded cholesterol level, which we'll call this value X, is was equal to 245 mg per deciliter. We're also told the mean cholesterol value in the mean, which will denote as mu, is equal to 195 mg per deciliter. And finally, we're also told the standard deviation, which will denote this as sigma, and sigma is equal to our standard deviation is equal to 30 mg per deciliter. Awesome. So our second step now is we need to compute the difference between the highest recorded cholesterol level and the mean cholesterol level, meaning we need to compute the difference D. So the difference D. is equal to x minus mu, which is equal to 245, then we need to take 245. And we need to subtract 195, so when we do that, we will get 50 mg per deciliter. Fantastic. Moving right along here. So our third and final step, we need to calculate how many standard deviations is that difference. So we need to find our Z score. So as we should recall, the Z score equation states that Z, the Z score is equal to X minus mu. Divided by sigma. And when we plug in our known variables, we will find that Z is equal to 50 divided by 30, which is equal to when we plug it into our calculator, 1.67. When we round to two decimal places, and that is our final answer. Hooray, we did it. So you could, to be more precise, write down your units into your equation for the Z score, but as you should notice, the units will cancel out, giving us a unitless answer. So that's how we get 1.67. Awesome. So looking at our multiple choice answers, our final answer has to be multiple choice answer letter D, which once again is 1.67. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Z-Scores

Mean

Standard Deviation

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