Question

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

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)

• 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,

P(17 < X-bar < 49) =

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