6.1 Quick revision

We strongly recommend trying these Quick revision questions before your tutorial.

A new method for evaluating bridge loads (O’Brien et al. 2018) used a simulation to compare the new method to an existing method. For the simulation, they modelled the gross vehicle mass (GVM) of trucks as having a normal distribution, with a mean of \(13\) tonnes and a standard deviation of \(1.3\) tonnes.

The Isuzu F-Series trucks are rated as having a GVM between \(10.7\) and \(26.0\) tonnes (depending on the configuration).

  1. What is the \(z\)-score for the lower limit of \(10.7\) tonnes?
  2. What is the \(z\)-score for the upper limit of \(26.0\) tonnes?
  3. What does a negative \(z\)-score mean?
  1. \(z = (10.7 - 13)\div 1.3 = -1.77\).
  2. \(z = (26.0 -13)/1.3 = 10\).
  3. A negative \(z\)-score means that the value is less than the mean.

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O’Brien EJ, Zhang L, Zhao H, Hajializadeh D. Probabilistic bridge weigh-in-motion. Canadian Journal of Civil Engineering. NRC Research Press; 2018;45(8):667–75.