Let assume that x ̅ ~ N (50, 2) and x ~ N (50, 20), which of the two distributions above will have a narrower spread and why? 1. The population distribution because its standard deviation (2) is smaller than the other (20). 2. Both are same spread because their standard deviations are 50. 3. Both are same spread because their means are 50. 4. The sampling distribution because its standard deviation (2) is smaller than the other (20).
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Let assume that x ̅ ~ N (50, 2) and x ~ N (50, 20),
which of the two distributions above will have a narrower spread and why?
| 1. |
The population distribution because its standard deviation (2) is smaller than the other (20). |
|
| 2. |
Both are same spread because their standard deviations are 50. |
|
| 3. |
Both are same spread because their means are 50. |
|
| 4. |
The sampling distribution because its standard deviation (2) is smaller than the other (20). |
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- Use Excels functions (not @RISK) to generate 1000 random numbers from a normal distribution with mean 100 and standard deviation 10. Then freeze these random numbers. a. Calculate the mean and standard deviation of these random numbers. Are they approximately what you would expect? b. What fraction of these random numbers are within k standard deviations of the mean? Answer for k = 1; for k = 2; for k = 3. Are the answers close to what they should be (about 68% for k = 1, about 95% for k = 2, and over 99% for k = 3)? c. Create a histogram of the random numbers using about 10 bins of your choice. Does this histogram have approximately the shape you would expect?What is the meaning of x ~ N (50, 20)? 1. Sampling distribution of x is distributed with a mean of 20 and a standard deviation of 50 2. x-bar is normally distributed with a mean of 20 and a standard deviation of 50 3. x is normally distributed with a mean of 50 and a standard deviation of 20 4. Sampling distribution of x is distributed with a mean of 50 and a standard deviation of 20What is the meaning of x ̅ ~ N (50, 2)? 1. The Sampling distribution is distributed normally with a mean of 50 and a standard deviation of 2 2. Sampling distribution of x is distributed normally with a mean of 2 and a standard deviation of 50 3. x is normally distributed with a mean of 50 and a standard deviation of 2 4. x-bar is normally distributed with a mean of 2 and a standard deviation of 50
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