The manufacturer of a new board game believes that the time it takes a child between the ages of 5 and 10 to learn the rules of this game has the probability density function\[ g(t) = \begin{cases} \frac{3}{32}(4t - t^2) & \text{when } 0 \leq t \leq 4 \\ 0 & \text{elsewhere} \end{cases} \]where $ t $ is time measured in minutes.**(a)** Calculate the mean time it takes a child age 5 to 10 to learn the rules of this game. (Round your answer to three decimal places.)\[ \text{min} \]**(b)** Calculate the standard deviation of the learning times. (Round your answer to three decimal places.)\[ \text{min} \]**(c)** Calculate $ P(t \leq 3) $. (Round your answer to three decimal places.)\[ \]Interpret this result. (Round your numerical answer to one decimal place.)There is a(n) \[ \%\] chance that the time it takes a child between the ages of 5 and 10 to learn the rules of this game is three minutes.

(a) The probability density function of the manufacturer of a new board game believes that the time…

(a) Calculate the mean time it takes a child age 5 to 10 to learn the rules of this game. (Round your answer to three decimal places.) min (b) Calculate the standard deviation of the learning times. (Round your answer to three decimal places.) min (c) Calculate P(t s 3). (Round your answer to three decimal places.) Interpret this result. (Round your numerical answer to one decimal place.) There is a(n) % chance that the time it takes a child between the ages of 5 and 10 to learn the rules of this game is ---Select--- three minutes.

(a) Calculate the mean time it takes a child age 5 to 10 to learn the rules of this game. (Round your answer to three decimal places.) min (b) Calculate the standard deviation of the learning times. (Round your answer to three decimal places.) min (c) Calculate P(t s 3). (Round your answer to three decimal places.) Interpret this result. (Round your numerical answer to one decimal place.) There is a(n) % chance that the time it takes a child between the ages of 5 and 10 to learn the rules of this game is ---Select--- three minutes.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

The manufacturer of a new board game believes that the time it takes a child between the ages of 5 and 10 to learn the rules of this game has the probability density function

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

where $ t $ is time measured in minutes.

**(a)** Calculate the mean time it takes a child age 5 to 10 to learn the rules of this game. (Round your answer to three decimal places.)

\[ \text{min} \]

**(b)** Calculate the standard deviation of the learning times. (Round your answer to three decimal places.)

\[ \text{min} \]

**(c)** Calculate $ P(t \leq 3) $. (Round your answer to three decimal places.)

\[ \]

Interpret this result. (Round your numerical answer to one decimal place.)

There is a(n) \[ \%\] chance that the time it takes a child between the ages of 5 and 10 to learn the rules of this game is three minutes.

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