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The length of time it takes a baseball player to swing a bat (in seconds) is...

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Statistics

The length of time it takes a baseball player to swing a bat (inseconds) is a continuous random variable X with probability densityfunction (p.d.f.) f(x) = ( ax + 8/9 for 0 ≤ x ≤ b

(c) Calculate (to 3 decimal places of accuracy) the median ofX.

(d) What is the probability that the baseball player takesbetween 5 and 10 swings (inclusive) before a swing whose length isgreater than the median in part (c) occurs for the first time?

(e) Over the next 36 (independent) swings that the baseballplayer takes, what is the approximate probability that the averageswing length is between 3/5 and 4/5 of a second?

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