Records show that the distance driven by a bus driver in a week is normally distributed with mean $1150{\text{ }}km$ and standard deviation $105{\text{ }}km$. New driving regulations are introduced and in the next 20 weeks he drives a total of $21800{\text{ }}km$.
a) Stating any assumption(s), test, at the 1% significance level, whether his mean weekly driving distance has decreased.
b) A similar test at the 1% significance level was carried out using the data from another 20 weeks. State the probability of a Type I error and describe what is meant by a Type I error in this context.
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