Question

Use the empirical rule to determine the approximate probability that a z value is between 0 and 1 on the standard normal curve.

Answer 1

You need to use a table of standar normal distribution curve. There are different kind of tables (cumulative, fi function, stc..), but your anwer is:
`P( 0 < z < 1) = 0.34`

The empirical rule allows you to make a quick assessment of probability without using a table. Just memorise these three numbers:

`0.34=34%` is less than one standard deviation `sigma` higher than the mean `mu`
`0.135=13.5` is between `sigma` and `2sigma` higher than `mu`
`0.025=2.5%` is more than `2sigma` higher than `mu`

The same goes for values below `mu`, as the normal curve is symmetrical. (So you have 68% of your values between `mu-sigma` and `mu+sigma`, or between `z=-1` and `z=+1`)

Remember every `sigma` translates to `1` on the `z`-scale