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A coffee vending machine dispenses a certain amount of coffee per press(purchase). If 35 cups of coffee are sampled and the amount of coffee dispensed

A coffee vending machine dispenses a certain amount of coffee per press(purchase). If 35 cups of coffee are sampled and the amount of coffee dispensed follows a normal distribution with an average of 590 ML and a standard deviation of 19.5ML

a) Can we assume the sampling distribution of sample means is normally distributed? Why?

b) What's the probability that in a second sample the mean will be less than 585 ML?

c) What is the probability that the mean of the 35 coffees is between585ML and 600 ML?

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