Question 1011534: The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.
a. 121.6, 152.4
b. 121.6, 150.4
c. 123,6, 150.4
d. 122.6, 148.4
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mean is 136
standard deviation is 12.
your confidence interval is .7698.
that's a two tailed confidence interval, so your alpha is (1 - .7698) / 2 = .1151.
that alpha would be on each end of the normal disribution curve.
you would look up a z-score with an area of .1151 to the left of it.
that's your low z-score.
you would look up a z-score with an area of .1151 to the right of it.
that equates to a z-score with an area of 1 - .1151 = .8849 to the left of it.
you can look these up in the z-score table, or you can use a calculator.
if you used the z-score table, you would find the z-scores to be between -1.2 and 1.2.
since these were found firectly from the table, the calculator should give you the same result.
i used my ti-84 plus and got z-score between -1.199843825 and 1.99843825.
this rounds to between -1.2 and 1.2, so the results are comparable, even though the calculator gets into more detail than the table.
the table i used can be found here:
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdfhttp://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
there is also an online z-score calculator that will find it for you and show you what it looks like graphically.
that calculator can be found here:
http://davidmlane.com/hyperstat/z_table.html
a picture of the results from your problem is shown below:
now you want to translate the z-score into a raw-score.
the formula for that is:
z = (x-m)/s
x is the z-score.
x is the raw score
m is the mean
s is the standard deviation.
in your problem:
z1 = -1.2 = the low z-score.
z2 = 1.2 = the high z-score.
x1 is the low raw score you want to find.
x2 is the high raw score you want to find.
m = 136 is the mean of the systolic blood pressure from all patients measured at the hospital.
s = 12 is the standard deviation.
a normal distribution is assumed.
the formula for the low score is z1 = (x1 - m) / s which is equal to -1.2 = (x1 - 136) / 12.
solve for x1 to get x1 = 12 * -1.2 + 136 = 121.6.
the formula for the high score is z2 = (x2 - m) / s which is equal to 1.2 = (x1 - 136) / 12.
solve for x2 to get x2 = 12 * 1.2 + 136 = 150.4
you have a low score of 121.6 and a high score of 150.4
that should be selection b.
a picture of what that looks like, using the online graphing calculator, is shown below:
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