The amount of water in a two-liter bottle is approximately normally distributed with a mean of 2.05 liters with a standard deviation of 0.025 liter.

a. What is the probability that an individual bottle contains less than 2.03 liters?

b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is less than 2.03 liters?

c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is less than 2.03 liters?

d. Explain the difference in the results in (a) and (c).

e. Explain the difference in the results in (b) and (c).