For the data in question 13, find the raw scores that correspond to the following:
(a) z 5 11.22; (b) z 5 20.48.
Z = (score-mean)/SD
Since I don't know the mean or SD, I can't help you find the raw score.
Also, your values don't make sense. Do you mean:
Z = 11.22 and Z = 20.48?
If so, those are extremely deviant values. If not, you need to clarify your data.
For the data,
9 5 10 7 9 10 11 8 12 7 6 9
To find the raw scores corresponding to specific z-scores, you need to use the formula for the z-score:
z = (x - μ) / σ
where:
- z is the z-score
- x is the raw score
- μ is the population mean
- σ is the population standard deviation
Given that you have the z-scores and not the mean and standard deviation, we need to use an alternate method to find the raw scores corresponding to these z-scores. We can accomplish this by using a z-table.
(a) To find the raw score corresponding to z = 11.22, follow these steps:
1. Locate the z-score of 11.22 in the z-table. Since most z-tables only go up to 3.49, you may need to use a calculator or software that can calculate the corresponding value for extremely high z-scores like 11.22.
2. Once you have the corresponding value from the table, convert it back to a raw score using the formula:
x = (z * σ) + μ
where:
- x is the raw score
- z is the z-score (11.22 in this case)
- σ is the population standard deviation (unknown in this case)
- μ is the population mean (unknown in this case)
(b) To find the raw score corresponding to z = 20.48, follow the same steps as above, using the z-score of 20.48.
Keep in mind that without the population mean and standard deviation, it is not possible to determine the exact values of the raw scores corresponding to these z-scores.