Question

X ~ N(50, 13). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums.

• Part (a)

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

  • A	B)
    C)D)

• Part (b)

  Give the distribution of X. (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, and find the probability. (Round your answer to four decimal places.)

  P(X < 50) = ________

• Part (d)

  Find the 30th percentile. (Round your answer to two decimal places.)

• _________.

• Part (e)

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

  P(48 < X < 54) = _________

• Part (f)

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

  P(17 < X < 48) = ___________

• Part (g)

  Give the distribution of ΣX.
  ΣX ~ ______(_____,_____)

• Part (h)

  Find the minimum value for the upper quartile for ΣX. (Round your answer to two decimal places.)

• ________.

• Part (i)

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

  P(1200 < ΣX < 1350) = ___________

Answer 1