Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.

a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)<br />
b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the
horizontal axis for X. Shade the region corresponding to the probability. Find the probability.<br />
c. Find the 80^th percentile of the distribution of the average of 49 fly balls

a. N(250, 50/sqrt(49)) = 0.42074

b. Calculate Z-score and probability = 0.08 shown here

c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) calculator
Using the Z-score formula, we have
0.8416 = (x - 250)/50
x = 292.08