Consultants employed by a large library reported that the time spent in the library by a user could be modelled by a normal distribution with mean 65 minutes and standard deviation 20 minutes.

(a) Assuming that this model is adequate, what is the probability that a user spends (i) less than 90 minutes in the library, (ii) between 60 and 90 minutes in the library? The library closes at 9.00p.m.

(b) Explain why the model above could not apply to a user who entered the library at 8.00 p.m.

(c) Estimate an approximate latest time of entry for which the model above could still be plausible. (AEB)