The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the probability that the sample mean will be
a) between 1.99 and 2.0 liters?
b) Below 1.98 liters
c) Greater than 2.01 liters?
d) The probability is 99% that the sample mean amount of soft drink will be at least how much?
e) The probability is 99% that the sample mean amount of soft drink will be between which two values (symmetrically distributed around the mean)?
Can you please show the work??