The duration, in days, of use of precision electronic scales before misalignment is modeled by a random variable $T$ which follows an exponential distribution with parameter $\lambda$. The representative curve of the density function of this random variable $T$ is given.
a. By graphical reading, give a bound for $\lambda$ with amplitude 0.01. b. The area of the shaded region, in square units, is equal to 0.45. Determine the exact value of $\lambda$.
In the following, we will take $\lambda = 0.054$.
Determine, to the nearest day, the average duration of use of a scale without it becoming misaligned.
A scale is put into service on January 1st, 2020. It operates without misalignment from January 1st to January 20 inclusive. Determine the probability that it operates without misalignment until January 31 inclusive.
The duration, in days, of use of precision electronic scales before misalignment is modeled by a random variable $T$ which follows an exponential distribution with parameter $\lambda$. The representative curve of the density function of this random variable $T$ is given.
\begin{enumerate}
\item a. By graphical reading, give a bound for $\lambda$ with amplitude 0.01.\\
b. The area of the shaded region, in square units, is equal to 0.45. Determine the exact value of $\lambda$.
\end{enumerate}
In the following, we will take $\lambda = 0.054$.
\begin{enumerate}
\setcounter{enumi}{1}
\item Determine, to the nearest day, the average duration of use of a scale without it becoming misaligned.
\item A scale is put into service on January 1st, 2020. It operates without misalignment from January 1st to January 20 inclusive. Determine the probability that it operates without misalignment until January 31 inclusive.
\end{enumerate}