## 6.1 Quick revision

We 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. A negative $$z$$-score means that the mean has a smaller value than the standard deviation. True of false?
4. A standard error measures the size of the difference between the sample proportion and the population proportion. True of false?
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.
4. The standard error measures how much a sample value is likely to vary from sample to sample.

### 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.