Suppose that the distance of fly balls hit to the outfield (in baseball) is norm

Question

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 42 feet. We randomly sample 49 fly balls. Part (a) If X = average distance in feet for 49 fly balls, then give the distribution of X. Round your standard deviation to two decimal places What is the probability that the 46 balls traveled an average of less than 242 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the 80th percentile of the distribution of the average of 49 fly balls. ()

Explanation / Answer

Part(b): Z is calculated as (242-250)/(42/sqrt(49))= -1.33

From normal distribution table you get 1-0.9082=0.0918 or 9.18%

Part(c): For 80%, look for 0.8000 in the normal distribution table and you get a Z value of 0.85

thus answer is 250+0.85*(42/sqrt(49)) =255.1

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