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 (a) above .10, (b) below .10, (c) above .20, (d) below .20, (e) above 1.10, (f) below 1.10, (g) above -.10, and (h) below -.10?
My goof. All you need to do is find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion and its Z score.
To find the percentages using a normal curve table, you need to convert the given Z-scores into standard scores (also known as z-scores) and then look up the corresponding areas under the curve.
Firstly, let's understand what a Z-score represents. In statistics, a Z-score measures how many standard deviations an individual score is from the mean of a distribution. A positive Z-score indicates a value above the mean, while a negative Z-score indicates a value below the mean.
Now let's calculate the percentages for each of the given Z-scores:
(a) To find the percentage above a Z-score of 0.10, this corresponds to finding the area to the right of 0.10 on the normal curve. To do this, you can subtract the area below 0.10 from 1 (the total area under the curve). For example, if the area below 0.10 is 0.4000, then the percentage above 0.10 is 1 - 0.4000 = 0.6000, or 60%.
(b) Similarly, to find the percentage below a Z-score of 0.10, you can directly look up the area below 0.10 on the normal curve. For example, if the area below 0.10 is 0.4000, then the percentage below 0.10 is 0.4000, or 40%.
(c) To find the percentage above a Z-score of 0.20, you can follow the same steps as in (a). Find the area below 0.20 and subtract it from 1 to get the percentage above 0.20.
(d) To find the percentage below a Z-score of 0.20, follow the same steps as in (b).
(e) To find the percentage above a Z-score of 1.10, again follow the steps as in (a).
(f) To find the percentage below a Z-score of 1.10, follow the steps as in (b).
(g) To find the percentage above a Z-score of -0.10, again follow the steps as in (a), but use the positive value of the Z-score.
(h) To find the percentage below a Z-score of -0.10, follow the steps as in (b), but use the positive value of the Z-score.
To find the exact areas under the curve for each Z-score, you can use a standard normal distribution table (also known as a Z-table). This table provides the area to the left of a given Z-score. To find the area to the right of a Z-score, you can subtract the table value from 1.
Note: The values given in this explanation are hypothetical for illustrative purposes only. You would need to refer to an actual Z-table to get the precise values for each Z-score.
You need to know the mean and standard deviation.
Z = (score-mean)/SD
18. 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?
You need to know the mean and standard deviation.
Z = (score-mean)/SD