6.1 Quick revision

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; in 2024).

What is the \(z\)-score for the lightest truck of \(10.7\) tonnes?
What is the \(z\)-score for the heaviest truck of \(26.0\) tonnes?
What does a negative \(z\)-score mean in this context?
True or false: A standard error measures the size of the difference between the sample proportion and the population proportion. Explain.

References

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.