Question: A normally distributed population has mean 57,800 and standard deviation 750.
a. Find the probability that a single randomly selected element X of the population is between 57,000 and 58,000.
b. Find the mean and standard deviation of X¯ for samples of size 100.
c. Find the probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000.