Question

X ~ N(50, 9). Suppose that you form random samples of 25 from this distribution.

Let X be the random variable of averages.

• Part (a)

  Sketch the distributions of X and X-bar on the same graph.

• Part (b)

  Give the distribution of X-bar.
  (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 for

  X-bar, and find the probability. (Round your answer to four decimal places.)

  P(X-bar < 50) =

• Part (d)

  Find the 10th percentile. (Round your answer to two decimal places.)

• Part (e)

  Sketch the graph, shade the region, label and scale the horizontal axis for

  X-bar, and find the probability. (Round your answer to four decimal places.)

  P(46 < X-bar < 52) =

• Part (f)

  Sketch the graph, shade the region, label and scale the horizontal axis for X-bar,
  and find the probability. (Round your answer to four decimal places.)

  P(17 < X-bar < 49) =

Answer 1