X~N(50,12). Suppose that you form random samples of 25 from this distribution. Let X (X with a line above it) be the random variable of averages. LetXbe the random variable of sums.

1. Sketch the distributions ofXandX (X with a line above it) on the same graph.

1. Give the distribution ofX. (X with a line over it) Enter an exact number as an integer, fraction, or decimal.)

X (With a line over it) ~ N ( ____, ____)

1. Sketch the graph, shade the region, label and scale the horizontal axis forX (with a line over it), and find the probability. (Round your answer to four decimal places.)

P (X < 50) = ______

1. Find the30thpercentile. (Round your answer to two decimal places.)

1. 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(48<X<54) =______

1. 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(19<X<46) =

1. Give the distribution ofX.

X~_____ (____, ____)

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

1. 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(1200<X<1350)