Standardization and Standard Normal Identification

Identify the distribution of a standardized variable Z = (X − μ)/σ as N(0,1) and/or use standardization as an explicit intermediate step to solve a problem.

bac-s-maths 2014 Q1C View
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 $\frac{T' - 15}{\sigma'}$
  1. What distribution does the random variable $Z'$ follow?
  2. Determine an approximate value to 0.01 of the standard deviation $\sigma'$ of the random variable $T'$.