2 In the past, the mean length of a particular variety of worm has been 10.3 cm , with standard deviation 2.6 cm . Following a change in the climate, it is thought that the mean length of this variety of worm has decreased. The lengths of a random sample of 100 worms of this variety are found and the mean of this sample is found to be 9.8 cm . Assuming that the standard deviation remains at 2.6 cm , carry out a test at the \(2 \%\) significance level of whether the mean length has decreased.
\(31.6 \%\) of adults in a certain town ride a bicycle. A random sample of 200 adults from this town is selected.

1. Use a suitable approximating distribution to find the probability that more than 3 of these adults ride a bicycle.
2. Justify your approximating distribution.