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A bottling company uses a filling machine to fill plastic bottles with popular cola. The contents...

A bottling company uses a filling machine to fill plastic bottles with popular cola. The contents are known to vary according to a normal distribution with mean μ = 300 ml and standard deviation σ = 10 ml. Show all your steps for full credit.

a. What is the probability that the mean contents of the bottles in a six pack is less than 295 ml?

b. Suppose we take a sample of two bottles. What's the probability that exactly one of them has the content less than 287 ml and another one is greater than 315 ml?

Math   Statistics-And-Probability   
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