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

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    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.

    a. If X = distance in feet for a fly ball, then X ~

    b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.

    c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.

    a. N(250, 50/sqrt(1))

    b. Calculate z-score
    Z = -0.6 and P(Z < -0.6) = 0.274253

    c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) calculator
    Z-score formula: 0.8416 = (x - 250)/50<br />
    x = 292.08

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