Find the standard normal area for each of the following, showing your reasoning clearly.

a. P(1.22<z<2.15)
b. P(2.00<z<3.00)
c. P(-2.00<z<2.00)
d. p(z=0.50)

a good place for playing around with Z table stuff is

http://davidmlane.com/hyperstat/z_table.html

how do I use it?

To find the standard normal area for each of the given probabilities, we will need to use the standard normal distribution table or a statistical software. The standard normal distribution table provides the areas under the curve to the left of a particular z-score.

For part a: P(1.22 < z < 2.15)
1. Look up the z-score for 1.22 in the standard normal distribution table. Let's say the corresponding area is A1.
2. Look up the z-score for 2.15 in the standard normal distribution table. Let's say the corresponding area is A2.
3. To find the area between the two z-scores, subtract A1 from A2: A2 - A1.

For part b: P(2.00 < z < 3.00)
Perform the same process as in part a to find the area between the two z-scores.

For part c: P(-2.00 < z < 2.00)
1. Look up the absolute values of the z-scores for -2.00 and 2.00 in the standard normal distribution table.
2. Find the area for each absolute z-score: A1 and A2.
3. To find the area between -2.00 and 2.00, subtract 2 times A1 from 1: 1 - (2 * A1) or subtract 2 times A2 from 1: 1 - (2 * A2). The result will be the same because the area to the left of a positive z-score is the same as the area to the right of its negative counterpart.

For part d: P(z = 0.50)
The probability of a specific z-score is 0 because the standard normal distribution is continuous. We can only find the probability of a range or an interval, not a single value.

Wow - you must give up easy.

For #a, click the Between button and enter the two values. Then click recalculate. It will show the relevant area and its probability: .0955

If you know the area and want the bounds, then click on the Value from an Area button.