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Sampling Distribution of Sample Mean

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I need help solving the following problem, please:

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 brobability 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 will contain at least how much soft drink?
e. The probibility is 99% that the sample mean will contain an amount that is between which two values (symmetrically distributed around the mean?

Thanks for your help!

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The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

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The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 litters and a standard deviation of 0.05 litres. If you select a random sample of 25 bottles, what is the probability that the sample mean will be
Answers
Let X be the fill amount of bottles of soft drink. Given that X is normal with mean µ = 2 and standard ...

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