4 Sasha tends to forget his passwords. He investigates whether the number of attempts he needs to log on to a system with a password can be modelled by a geometric distribution. On 55 occasions he records the number of attempts he needs to log on, and the results are shown in the table. Number of attempts 2 3 4 or more Frequency 20 19 13 3 (a) Test at the 1% significance level whether the results are consistent with the distribution Geo(0.4). 191 (b) Suggest which two probabilities should be changed, and in what way, to produce an improved model. (Numerical values are not required.) You should give a reason for your suggestion. [3]