Question 1118613: Determine the value of z so that the area under the standard normal curve
(a) in the right tail is 0.0305. Round the answer to two decimal places.
z =
(b) in the left tail is 0.0410. Round the answer to two decimal places.
z =
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! using the TI-84 Plus calculator, i get the following:
an area of .0305 to the right of the desired z-score gives you an area of 1 - .0305 = .9695 to the left of the desired z-score.
an area of .9695 to the left of the desired z-score gives you a z-score of 1.873495455.
round that to 2 decimal digits and the desired z-score with an area of .0305 to the right of it is 1.87.
an area of .0410 to the left of the desired z-score gives you a z-score of -1.739197665.
round that to 2 decimal digits and the desired z-score with an area of .0410 to the left of it is -1.74.
if you used the following z-score table, you would have found the following:
http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf
an area of .0305 to the right of the desired z-score is the same as an area of 1 - .0305 = .9695 to the left of it.
the z-score table would show you that:
a z-score of 1.87 has an area of .9693 to the left of it.
a z-score of 1.88 has an area of .9699 to the left of it.
since .9693 is closer to .9695, you would choose the z-score of 1.87.
since the normal distribution table is symmetric about the mean, you could also have done the following:
find the z-score with an area of .0305 to the left of it and then change the sign.
you would have found:
a z-score of -1.87 has an area of .0307 to the left of it.
a z-score of -1.88 has an area of .0301 to the left of it.
since .0307 is closer to .0305, you would have chosen -1.87 and changed the sign to get a z-score of 1.87 with an area of .0305 to the right of it.
to find the area of .0410 to the left of the desired z-score, you would look for an area of .0410 to the left of it in the same z-score table.
you would have found:
a z-score of -1.73 has an area of .0418 to the left of it.
a z-score of -1.74 has an area of .0409 to the left of it.
since .0409 is closer to .0410, you would have selected -1.74.
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