Final answer:
The sampling distribution of the mean will be normally distributed as the sample is drawn from a normally distributed population and the sample size is sufficiently large.
Step-by-step explanation:
Yes, the condition that Þxe is normally distributed is satisfied. This is because the population from which the sample is drawn is normally distributed, and the sample size (n = 20) is sufficiently large for the Central Limit Theorem to apply.
Since we also know the population standard deviation (3.2), this means we can use the standard normal distribution, or z-test, for hypothesis testing.