Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table, what percentage of architects have Z-scores:
Above .10 =
Below .10 =
Above .20 =
Below .20 =
Above 1.10 =
Below 1.10 =
Above -.10 =
Below -.10 =
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores. Multiply each by 100 to get percentages.
I assume you can find the table. We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
To find the percentage of architects with specific Z-scores using a normal curve table, follow these steps:
1. Convert the given Z-score to a standardized normal distribution value.
- To convert a positive Z-score, find the corresponding percentage from the table.
- To convert a negative Z-score, subtract the corresponding percentage from 1.
2. Multiply the converted percentage by 100 to express it as a percentage.
Here are the answers for the given Z-scores:
Above 0.10:
- Since the Z-score is positive, find the corresponding percentage from the normal curve table. The closest value is 0.5400.
- Multiply 0.5400 by 100 to get 54%.
- Therefore, approximately 54% of architects have Z-scores above 0.10.
Below 0.10:
- Since the Z-score is negative, subtract the corresponding percentage from 1. The closest value from the table is 0.4600.
- Subtracting 0.4600 from 1 gives 0.5400.
- Multiply 0.5400 by 100 to get 54%.
- Hence, approximately 54% of architects have Z-scores below 0.10.
Above 0.20:
- Using the same process, find the closest percentage from the table for a positive Z-score of 0.20, which is 0.5793.
- Multiply 0.5793 by 100 to get 57.93%.
- Therefore, approximately 57.93% of architects have Z-scores above 0.20.
Below 0.20:
- For a negative Z-score, subtract the corresponding percentage from 1. The closest value from the table is 0.4207.
- Subtracting 0.4207 from 1 gives 0.5793.
- Multiply 0.5793 by 100 to get 57.93%.
- So, approximately 57.93% of architects have Z-scores below 0.20.
Above 1.10:
- The closest percentage from the table for a positive Z-score of 1.10 is 0.8643.
- Multiply 0.8643 by 100 to get 86.43%.
- Hence, approximately 86.43% of architects have Z-scores above 1.10.
Below 1.10:
- For a negative Z-score, subtract the corresponding percentage from 1. The closest value from the table is 0.1357.
- Subtracting 0.1357 from 1 gives 0.8643.
- Multiply 0.8643 by 100 to get 86.43%.
- Therefore, approximately 86.43% of architects have Z-scores below 1.10.
Above -0.10:
- Since the Z-score is positive, find the corresponding percentage from the normal curve table. The closest value is 0.5398.
- Multiply 0.5398 by 100 to get 53.98%.
- Therefore, approximately 53.98% of architects have Z-scores above -0.10.
Below -0.10:
- Since the Z-score is negative, subtract the corresponding percentage from 1. The closest value from the table is 0.4602.
- Subtracting 0.4602 from 1 gives 0.5398.
- Multiply 0.5398 by 100 to get 53.98%.
- Therefore, approximately 53.98% of architects have Z-scores below -0.10.