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

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

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

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

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

Expert Solution

orchestra answered 11 months ago

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