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Mean and standard deviation of sample means

AP.STATS: UNC‑3 (EU), UNC‑3.Q (LO), UNC‑3.Q.1 (EK), UNC‑3.Q.2 (EK)
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Problem

A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an
SRS
of bulbs, and we calculate the sample mean lifetime x, with, \bar, on top of the bulbs in each package.
Calculate the mean and standard deviation of the sampling distribution of x, with, \bar, on top.
mu, start subscript, x, with, \bar, on top, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
hours
sigma, start subscript, x, with, \bar, on top, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
hours
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