Measurements of position

Hmmm. Z values. Percentile ranks. Proportions between two x-values.
How are these connected for Normal distributions?

The percentile for a particular z-value is the value in the body of the Z table that represents the "sum" of the column and row titles. For Negative z-values, just append (attach) the hundredths place digit. For instance. . .
row 1.3, column 0.4 ==> 1.34 = z. This is the 90.99th percentile.
for row -2.3, column 0.4 ==> -2.34 = z. With a table value if 0.0096, this is just a hair under the 1st percentile.

The percentile is the proportion of data that lies to the left of the x value or is equal to it. If you took a test and scored at the 99th percentile, 99% of all other test scores should be equal to your score or below it.

Another way to find the percentile is to use the NormalCDF function on the calculator. Use NormalCDF(lower bound, upper bound) where the boundary values are z scores. To find the percentile for a Normally-distributed z value, we use the lower bound of negative infinity and the upper bound of the z under consideration.

We can use -999999 for negative infinity. NormalCDF(-999999,1) = the proportion of the population of Normally distributed z values that fall equal to or below 1.

To find the Z value for a particular percentile, use the inverse of the NormalCDF function-- INVNorm. To find the 95th percentile, enter InvNorm(.95). Approximately 95% of all z-values in a Normal distribution will fall below this value.

To find the X value that corresponds to the desired Z value, take the mean and add Z standard deviations.

Practice converting X values into z values adn percentiles into X values. Do the problems on page 147.