Posted by Devon on Monday, September 10, 2007 at 7:24pm.
It helps to know how to read a z-table to answer these kinds of questions.
For part A, you will need to find a z value where 80% is below the z and 20% is above the z. Remember that the mean divides the distribution in half: 50% is below the mean and 50% is above the mean. Therefore, 80% is above the mean and you will have to look within the table at .30 (most tables go out to 4 places after the decimal point, so the table might show .3000) or closest to that value to find the z if your table shows from mean to z values. Tables can be set up differently, so be mindful of that when you look for these values.
For part B, you will need to find a z value where 65% is below the z and 35% is above the z. Therefore, in a table that shows from mean to z values, you will look for .15 (or .1500) in the table to find the z.
Both z values will be positive because they are above the mean of the distribution. (Negative z values are below the mean of the distribution.)
I hope this will help.
Find the number z such that 35% of all observations from a standard Normal distribution are greater than z
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