A machine automatically dispenses a beverage of a desired size. When set to "small," the machine dispenses varying amounts of liquid with a mean of 275\,\text{mL}275mL275, start text, m, L, end text and standard deviation of 10\,\text{mL}10mL10, start text, m, L, end text. Suppose that we take random samples of 555 of these drinks and calculate the mean amount of liquid \bar x
x
ˉ
x, with, \bar, on top in each sample. We can assume that individual drinks are independent.
Calculate the mean and standard deviation of the sampling distribution of \bar x
x
ˉ
x, with, \bar, on top.
You may round to one decimal place.

Question

07-03-2021
Advanced Placement (AP)

Answered

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A machine automatically dispenses a beverage of a desired size. When set to "small," the machine dispenses varying amounts of liquid with a mean of 275\,\text{mL}275mL275, start text, m, L, end text and standard deviation of 10\,\text{mL}10mL10, start text, m, L, end text. Suppose that we take random samples of 555 of these drinks and calculate the mean amount of liquid \bar x
x
ˉ
x, with, \bar, on top in each sample. We can assume that individual drinks are independent.
Calculate the mean and standard deviation of the sampling distribution of \bar x
x
ˉ
x, with, \bar, on top.
You may round to one decimal place.

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