Math Solutions

(Solution Library) Learning Time The manufacturer of a new board game believes that the time it takes a child between the ages of 8 and 10 to learn the rules

Question: Learning Time The manufacturer of a new board game believes that the time it takes a child between the ages of 8 and 10 to learn the rules of its new board game has the probability density function

\[P(t)= \begin{cases}\frac{3}{32}\left(4 t-t^{2}\right) & \text { when } 0 \leq t \leq 4 \\ 0 & \text { when } t>4\end{cases}\]

where \(t\) is time measured in minutes.

  1. Find the mean time that it takes a child age 8 to
    10 to learn the rules of the game.
  2. Find the standard deviation of the learning times.
  3. Find \(P(0 \leq t \leq 1.5)\). Interpret this result.
  4. Find \(P(t \geq 3) .\) Interpret this result.

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