| MATH 924 | | | NAME: |
| HOMEWORK ASSIGNMENT #1, CLASS 4 |
| WORKING WITH THE Z-TABLE |
| TASK: DETERMINE THE PROBABILITY P AND % CHANCE THAT A Z VALUE LIES +/- 1, +/- 1.5, +/-2, +/-2.5 OR +/-3 |
| STANDARD DEVIATIONS FROM THE POPULATION MEAN |
| Comment: For 1, 2, and 3 σ from the mean this calculation will result in the values for the empirical rule . |
| TIP: this is an "in between" probability with z1 being -1, -1.5, -2, -2.5, or -3 and z2 being +1, 1.5, 2, 2.5 or 3 |
| (see slide 7) |
| Simplification/special case (see figure below): |
| Since the z distribution is symmetrical, the "less than" z1 area has the same probability than the |
| "greater than" z2 area. |
| Therefore, to find the area between z1 and z2 you just have to subtract 2x p"less than" z1 from 1. |
| z1 | p "less than" z1 | p "greater than z2" | Overall p | % CHANCE |
| | area to the left of z1 | area to the right of z2 | area from -z to + z |
| | | (same as p "less than" |
| | from z table | z1, can leave blank) | p = 1 - (2 x p"less than" z1) | [column G x 100] |
| -1 |
| -1.5 |
| -2 |
| -2.5 |
| -3 |
| Note: It is critical that you look up z1 in the table (the negative z) and not z2 (the positive z). |
| Since the table shows the probability LEFT of z, the values for z2 would be very large, |
| encompassing the area to the left of z2 and not to the right of z2. |
| ANOTHER NOTE (to explain why the above strategy is different than the one shown in the lecture): |
| The calculation strategy outlined above only works if z1 has the same distance from 0 than z2 (that is z1 and z2 are equal to +/- any number), |
| which is the case in the assigned calculations above. |
| In order to calculate the probability that a z value lies between any two given z values, |
| you need to use the strategy for "in between" probabilities given in Lecture 4 slide 7: |
| calculate area under the curve up to z2 and subtract area under the curve up to z1. |
| If you try this strategy for the above numbers, you will get the same result. |
| That is, look up p for z=+1 and subtract p for z=-1; look up p for z +2 and subtract p for z=-2, etc. |
pbiner
CLASS4HWASSIGNMENT1.xlsx
