At a certain shop, customers arrive independently and randomly at a constant average rate of 23.4 per hour.

(a) Find the probability that, in a randomly chosen 1-minute period, at least 2 customers arrive. [3]

(b) The random variable \(X\) denotes the number of customers who arrive in a randomly chosen 1-hour period.

(b(i)) State a suitable approximating distribution for \(X\), giving the value(s) of any parameter(s). [2]

(b(ii)) Use your approximating distribution to find \(\mathrm P(20<X<30)\). [3]