Final answer:
To generate samples of size 4 from normally distributed populations, assume a mean if not given and use the standard deviation provided to select z-scores, which can then be scaled to create the sample.
Step-by-step explanation:
To generate a sample of size 4 from each described population being normally distributed and assuming independent populations, we can follow these steps:
- For the population with a standard deviation of 4: Assume a mean (which is not provided) and use the standard normal distribution to select four values (e.g., z-scores) that are then scaled based on the standard deviation.
- For the population with a mean of 125 and standard deviation of 7: Select four values using the normal distribution centered around 125, each spread out by 7 units of standard deviation.
- For the population with a mean of 75 and standard deviation of 4.5: Follow a similar approach to the above populations, centering around 75 and using 4.5 as the spread of values.
Example samples, assuming a mean (where not provided), could be:
- Sample for population with standard deviation 4 (mean assumed as 100): 98, 102, 101, 96.
- Sample for population with mean 125 and standard deviation 7: 127, 122, 120, 130.
- Sample for population with mean 75 and standard deviation 4.5: 77, 72, 74, 79.
The examples provided are fictional and are used to demonstrate the process of generating samples from normal distributions with specified standard deviations and means.