5 The distance driven in a week by a long-distance lorry driver is a normally distributed random variable with mean 1850 km and standard deviation 117 km .
- Find the probability that in a random sample of 26 weeks his average distance driven per week is more than 1800 km .
- New driving regulations are introduced and in a random sample of 26 weeks after their introduction the lorry driver drives a total of 47658 km . Assuming the standard deviation remains unchanged, test at the \(10 \%\) level whether his mean weekly driving distance has changed.