When you know the proportion, but you don’t know the x-value that represents the
cut-off, you need to use Table A backward.
Finding a value given a proportion
1.State
the problem and draw a picture.
2.Use Table A backward, from the inside out
to the margins, to find the corresponding z.
3.Unstandardize to transform z back to
the original x scale by using the formula:
We do this by
standardizing the distributions - really all this is redefining them not
changing the shape but the bottom axis so that instead of being N(mu, sigma)
they are N(mean =0,sd=1), and the bottom axis is in terms of the SD rather
than the Height.
You get this by
calculating a value z for every point in x your data set. If you were to then
draw the density curve for the z values you get a curve with a mean of 0 and
a sd of 1.Once you have standardized,
you can look up any value you want using a table. So, for instance, we knew
that 68% of women were between 62 and 67 inches tall from knowing simple
rules about 1,2,3 sd from mean. But if wanted to know the percentage of women
that were less than 63 inches tall. Can’t just use those rules. need to
standardize and go to table A - standard normal probabilities - on green card
in book or in back. First standardize x to get z, thenumber of sd from the mean. It is 0.6 to the
left (is negative).Look for -0.6 in
left column (z), and then going across row, under .00 column (no more
decimals on (-0.6) you find .2743.Twenty seven percent of women are shorter than 62 inches tall.