When the student uses the bus, his travel time, expressed in minutes, between his home and his school is modeled by a random variable $T'$ which follows a normal distribution with mean $\mu' = 15$ and standard deviation $\sigma'$. We know that the probability that it takes him more than 20 minutes to get to his school by bus is 0.05. We denote by $Z'$ the random variable equal to $\frac{T' - 15}{\sigma'}$
- What distribution does the random variable $Z'$ follow?
- Determine an approximate value to 0.01 of the standard deviation $\sigma'$ of the random variable $T'$.