Do you understand z-scores? I need help?

Question

I need the answers to the following questions, but I'd also like to understand the concepts more. So, the more information you can provide the better. Thank you in advance!


(1.) True or False - Jerry Whitecloud just threw a baseball 92 miles per hour. The mean speed of all the other players on the team is 84 miles per hour, and the standard deviation is 4. Jerry’s z-score is 2.


(2.) The relationship between the empirical rule and a z-score would indicate that any z-score between –2 and 2 will occur about ___________ percent of the time.
a.1
b.5
c.32
d.95


(3.) Karl Schmidt just scored a 96 on his last biology unit test. The mean score of the 36 students in his class was 78, and the standard deviation was 12. What is Karl’s z-score?
a.0.5
b.1.0
c.1.5
d.4.8

Answer 1

1. A z score is calculated by: (X-mean)/standard deviation
So Jerry's speed (92) = X the average (=mean is 84) and the standard deviation is 4
Z = (92-84)/4 = 8/4 = 2
It is TRUE Jerry's z-score is 2.

2. The empirical rule is that 68% of values fall within 1 std. dev. of the mean. Then 95% within 2 std. dev.s. And then that 99.5% are within 3 std. dev.s.
So since Z-scores follow a normal with mean=0 and variance = 1, the standard deviation = 1. So numbers from -2 to 2 will happen 95% of the time according to the empirical rule.

3. Z = (X-mean)/std. dev. = (96-78)/12 = 18/12 = 1.5

Answer 2

basically, a z-score is how many standard deviations away from the mean a certain datum is. so what you do to find a z-score is find out how far away from the mean it is, and divide by the standard deviation (which is adjusted for sample size by dividing it by the square root of the sample size):

in the example of the baseball:

z = 92 (jerry's speed) - 84 (mean speed of team) / 4 (standard deviation)
= 8 / 4 = 2 (true)

about the empirical rule, about 68% of all values fall within 1 standard deviation of the mean, about 95% fall within 2 standard deviations of the mean, and about 99% fall within 3 standard deviations of the mean.

Answer 3

Basically, the z score tells you how far (in standard deviations) a given score is from the mean for the group.

It's a way to compare standing from situation to situation, by standardizing the values (so you can see how far out a number is, no matter what the mean and standard deviation are -- how far out is this from the group's middle, is it in a tail, or near the middle; no matter what the mean and spread, you get a sense of how unusual that person (or whatever) is.

Hope that helps.

Try reviewing the definition and calculations of z score, and see if my answer helped.

Answer 4

nicely first locate the equation. My memory tells me it truly is (fee (to that end each and each and absolutely everyone temperature you want to transform) - recommend)/ popular deviation. So... because the animal has a body temp of ninety 3.31, the recommend is ninety 3.31; popular deviation is .76. So for the first decision, ninety 2.61, we would do: (ninety 2.61 - ninety 3.31)/.76 = -.097, that's the z-score fee. Z-rankings inform you the way many popular deviations you're from the recommend, and ninety 3.31 minus one popular deviation is ninety 3.31 - .76 = ninety 2.fifty 5, that's enormously on the point of ninety 2.61. Make sense, good? if you may do one, you are able to surely do the others, and that i do not favor to do your homework for you (sorry about the cynicism!), so with any luck I helped!