The incubation time, expressed in hours, of the virus can be modeled by a random variable $T$ following a normal distribution with standard deviation $\sigma = 10$. We wish to determine its mean $\mu$.
a. Conjecture, using the graph of the probability density function, an approximate value of $\mu$. b. We are given $P(T < 110) = 0.18$. Shade on the graph a region whose area corresponds to the given probability.
We denote by $T'$ the random variable equal to $\frac{T - \mu}{10}$. a. What distribution does the random variable $T'$ follow? b. Determine an approximate value to the nearest unit of the mean $\mu$ of the random variable $T$ and verify the conjecture from question 1.
The incubation time, expressed in hours, of the virus can be modeled by a random variable $T$ following a normal distribution with standard deviation $\sigma = 10$. We wish to determine its mean $\mu$.
\begin{enumerate}
\item a. Conjecture, using the graph of the probability density function, an approximate value of $\mu$.\\
b. We are given $P(T < 110) = 0.18$. Shade on the graph a region whose area corresponds to the given probability.
\item We denote by $T'$ the random variable equal to $\frac{T - \mu}{10}$.\\
a. What distribution does the random variable $T'$ follow?\\
b. Determine an approximate value to the nearest unit of the mean $\mu$ of the random variable $T$ and verify the conjecture from question 1.
\end{enumerate}