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Sports and Leisure

A recent study investigated the association between heading a soccer ball and subclinical evidence of traumatic brain injury.5 Amateur soccer players were selected, and each completed a questionnaire to determine the number of times (x) they headed the ball in the last 12 months. In addition, each player was subject to diffusion-tensor magnetic resonance to measure the fractional anisotropy (FA, y). Suppose the estimated regression line was y = 20.00026x + 0.6877.

a. Find the expected value of y if the number of headers is 1000.

b. Find an estimate of an observed y value for x = 1200.

c. Suppose σ = 0.06. Find the probability that an observed y value is more than 0.5 when the number of headers is 750.

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