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; in 2024).

1. What is the $z$-score for the lower limit of $10.7$ tonnes? 1.77-1.77-0.70.7
2. What is the $z$-score for the upper limit of $26.0$ tonnes? 10-10-1616
3. What does a negative $z$-score mean?
   There has been an errorThe mass is larger than averageThe mass is lower than averageThe mass is a negative number, which is impossible

0 of 3 correct

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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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.

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