SOLUTION: Round each z-score to the nearest hundredth. A data set has a mean of x = 214 and a standard deviation of 48. Find the z-score for each of the following. (a) x = 200 (b

Algebra ->  Probability-and-statistics -> SOLUTION: Round each z-score to the nearest hundredth. A data set has a mean of x = 214 and a standard deviation of 48. Find the z-score for each of the following. (a) x = 200 (b      Log On


   



Question 1156138: Round each z-score to the nearest hundredth.
A data set has a mean of
x = 214
and a standard deviation of 48. Find the z-score for each of the following.
(a)
x = 200
(b)
x = 224
(c)
x = 300
(d)
x = 100

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
You are asked to change from numbers on the x-axis on the first graph below
to their corresponding numbers on the z-axis on the second graph below. 

On the first graph below, the mean 214 is in the middle.  Then 214 plus the
standard deviation 48 is added over and over: 214+48=262 is the first number
marked right of the mean, then 262+48=310, etc. on the right of the mean 214,
and 214-48=166, then 166-48=118, etc. on the left of the mean 214.  

Here is the x-axis of actual values which we denote by x or X:


    22    70   118   166   214   262   310   358   406    x
 
We change the values of the actual x-axis values to the z-axis values below,
which we call "z-scores" of the x-values above on the x-axis. The z-scores on
the z-axis below are the codings of the original x-values that tell us how many
times the standard deviation is added to or subtracted from the mean in the
actual x-value to get the z-score corresponding to that x-value.


   -4    -3    -2    -1     0     1     2     3     4     z

(a)
x = 200

We use the formula z=%28x-mu%29%2Fsigma=%28200-214%29%2F48=-0.2916666667
which we round off to -0.29, which means that the original x-value of
200 on the x-axis of the first graph above corresponds to the z-score
of -0.29 on the z-axis of the second graph above.

(b)
x = 224

We use the formula z=%28x-mu%29%2Fsigma=%28224-214%29%2F48=-0.2083333333
which we round off to -0.21, which means that the original x-value of
224 on the x-axis of the first graph above corresponds to the z-score
of -0.21 on the z-axis of the second graph above.

(c)
x = 300

We use the formula z=%28x-mu%29%2Fsigma=%28300-214%29%2F48=1.791666667
which we round off to 1.79, which means that the original x-value of
300 on the x-axis of the first graph above corresponds to the z-score
of 1.79 on the z-axis of the second graph above.

(d)
x = 100

You do that one yourself. And please learn HOW to calculate the z-score,
and ESPECIALLY, learn what it MEANS.  They call it the "z-axis" and the
values on it "z-scores" because it has "zero" corresponding to the mean 
value and "zero" begins with "z".

Edwin