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?
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To determine the percentages of architects with specific Z-scores using a normal curve table, we need to find the area under the normal distribution curve corresponding to those Z-scores.
1. Above 0.10:
To find the percentage of architects with Z-scores above 0.10, we need to calculate the area to the right of this Z-score. This can be done by subtracting the area to the left of 0.10 from 1. Since the normal distribution is symmetric, we can directly look up the value in the standard normal distribution table. From the table, the area to the left of 0.10 is approximately 0.5398. Subtracting this from 1, we get 1 - 0.5398 = 0.4602, or 46.02% of architects have Z-scores above 0.10.
2. Below 0.10:
To find the percentage of architects with Z-scores below 0.10, we can directly look up the area to the left of 0.10 in the standard normal distribution table. From the table, the area to the left of 0.10 is approximately 0.5398, or 53.98% of architects have Z-scores below 0.10.
3. Above 0.20:
Similarly, to find the percentage of architects with Z-scores above 0.20, we can calculate the area to the right of this Z-score. Looking up the value in the standard normal distribution table, the area to the left of 0.20 is approximately 0.5793. Subtracting this from 1, we get 1 - 0.5793 = 0.4207, or 42.07% of architects have Z-scores above 0.20.
4. Below 0.20:
To find the percentage of architects with Z-scores below 0.20, we can directly look up the area to the left of 0.20 in the standard normal distribution table. From the table, the area to the left of 0.20 is approximately 0.5793, or 57.93% of architects have Z-scores below 0.20.
5. Above 1.10:
To find the percentage of architects with Z-scores above 1.10, we can calculate the area to the right of this Z-score. Looking up the value in the standard normal distribution table, the area to the left of 1.10 is approximately 0.8643. Subtracting this from 1, we get 1 - 0.8643 = 0.1357, or 13.57% of architects have Z-scores above 1.10.
6. Below 1.10:
To find the percentage of architects with Z-scores below 1.10, we can directly look up the area to the left of 1.10 in the standard normal distribution table. From the table, the area to the left of 1.10 is approximately 0.8643, or 86.43% of architects have Z-scores below 1.10.
7. Above -0.10:
To find the percentage of architects with Z-scores above -0.10, we can calculate the area to the right of this Z-score. Looking up the value in the standard normal distribution table, the area to the left of -0.10 is approximately 0.4602. Subtracting this from 1, we get 1 - 0.4602 = 0.5398, or 53.98% of architects have Z-scores above -0.10.
8. Below -0.10:
To find the percentage of architects with Z-scores below -0.10, we can directly look up the area to the left of -0.10 in the standard normal distribution table. From the table, the area to the left of -0.10 is approximately 0.4602, or 46.02% of architects have Z-scores below -0.10.
Please note that these values are approximations as the standard normal distribution table typically provides values rounded to a certain number of decimal places.