Question 204556This question is from textbook thinking mathmatically
: This question is about using a z-table.
Use a z-table to find the specified area.
a.To the left of z=1.13
b.To the right of z=-1.82
I have the table but do not understand the question. On the test it will be multiple choice but I do not even know what to look for . Your help is greatly appreciated.
This question is from textbook thinking mathmatically
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your z score table should tell you the area under the normal probability distribution curve either to the left of the z-score or to the right of the z-score.
for example, the z-table in the following web address tells the area to the left of the z-score.
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http://lilt.ilstu.edu/dasacke/eco148/ZTable.htm
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your first problem is to find the area to the left of z = 1.13.
you can do this directly using this table because this table is telling you the area under the curve to the left of the z-score.
you find 1.1 in the vertical index and .03 in the horizontal index.
the area to the left of a z-score of 1.13 would be .8708 meaning that a z-score of 1.13 is higher than 87.08% of the population scores.
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your second problem is to find the area to the right of z = -1.82
you can do this indirectly using the same table.
look for the z-score of -1.82.
that would be -1.8 on the vertical index and .02 on the horizontal index.
the area to the left of a z-score of -1.82 would be .0344 meaning that a z-score of -1.82 is higher than 3.44% of the population.
Since they wanted the area to the right of -1.82, and this is showing you the area to the left of -1.82, you need to take 1 - the number shown to get the area to the right of -1.82. 1 - .0344 = .9656 meaning that the z-score of -1.82 is less than 96.56% of the population scores.
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if you use an online z-score calculator you can see this graphically.
one such calculator can be found at the following website.
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http://davidmlane.com/hyperstat/z_table.html
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there are two tables at this website.
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use the top table.
enter the mean of 0
enter the standard deviation of 1
enter 1.13 in the below selection box which means area under the curve to the left of the value.
the answer is automatically displayed as .870762. it agrees with the value of .8708 derived from the table but carries it out to more decimal places.
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use the top table again.
enter -1.82 in above selection box which means area under the curve to the right of the value.
the answer is automatically displayed as .965620. it agrees with the value of .9656 derived from the table but carries it out to more decimal places.
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it's a lot easier to use then the manual table and it's a good way to check if your use of the manual table is accurate.
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