## 6.1 Quick revision

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

A new method for evaluating bridge loads 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.

### 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.