) If this data were normally distributed, determine the probability that the sample mean would be as far away from the population mean or more so

To determine the probability that the sample mean would be as far away from the population mean or more so, we need to calculate the z-score and then find the corresponding probability from the standard normal distribution.

Here are the steps to follow:

1. Gather the necessary information:
- Population mean (μ)
- Population standard deviation (σ)
- Sample size (n)
- Distance between sample mean and population mean (d)

2. Calculate the standard error of the mean (SEM):
SEM = σ / √n

3. Calculate the z-score:
z = (d - 0) / SEM

4. Look up the z-score in a standard normal distribution table or use a statistical calculator to find the corresponding probability.

Note: For this calculation to be valid, the data must be normally distributed or the sample size must be large enough (usually n ≥ 30) for the Central Limit Theorem to apply.

Keep in mind that the probability obtained represents the probability of obtaining a sample mean as far away from the population mean or more extreme, assuming the data were normally distributed.