Question: X ~ N (60,11). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Sketch the

X~N(60,11).

Suppose that you form random samples of 25 from this distribution. LetX

be the random variable of averages.

  • Sketch the distributions ofXandX on the same graph.

  • Part (b)
  • Give the distribution ofX.(Enter an exact number as an integer, fraction, or decimal.)
  • X~

,

  • Part (c)
  • Sketch the graph, shade the region, label and scale the horizontal axis forX,
  • and find the probability. (Round your answer to four decimal places.)
  • P(X<60) =
  • Part (d)
  • Find the30thpercentile. (Round your answer to two decimal places.)
  • Part (e)
  • Sketch the graph, shade the region, label and scale the horizontal axis forX,
  • and find the probability. (Round your answer to four decimal places.)
  • P(58<X<64) =
  • Part (f)
  • Sketch the graph, shade the region, label and scale the horizontal axis forX,
  • and find the probability. (Round your answer to four decimal places.)
  • P(25<X<57) =

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