*[sorry, looks like I missed the “Publish” button again. I’m just posting this on Sunday instead of Friday :(]*

We practised a bunch with the z-score formula and relating small questions to the graph of the normal curve. Here are the problems to solve for homework:

- For a normal distribution with find .
- For a normal distribution with find so that .
- For a normal distribution with find .

## Spoiler Alert: Solutions

- Use the z-score formula to find . In the table look up the z-score 1.20 to find or 88.49%. [
**Some interpretations:**Graphically this means that 88.49% of the area under the normal curve is to the*left*of 112. In a survey this means that if you select a participant at random there is an 88.49% chance their “value” will be less than 112.] - Use the Standard Normal Probabilities table to find the z-score closest to 90%, or .9000 (we use 90% because we want the value that gives us , not less than . The probabilities in our table are .8997 and .9015, so .8997 is closest to 90%. That z-score is 1.28. Now, use that z-score with the z-score formula to solve for the missing value .
- and , so . [
**Note:**this is the same as . We’ll talk about this more on Monday.]