Alan is a member of an athletics club. In long jump competitions, his jumps are normally distributed with a mean of 7.6 m and a standard deviation of 0.16 m.

(a) Calculate the probability of him jumping (i) more than 8.0 m, (ii) between 7.50 m and 7.75 m.

(b) Determine the distance exceeded by 75% of his jumps. Brian also belongs to the athletics club. In long jump competitions, his jumps are normally distributed with a mean of 7.45 m and 95.2% of them exceed 7.0 m.

(c) Calculate, correct to two decimal places, the standard deviation of Brian's jumps. The athletics club has to select either Alan or Brian to be its long jump competitor at a major athletics meeting. In order to qualify for the final rounds of jumps at the meeting, it is necessary to achieve a jump of at least 8.0 m in the preliminary rounds.

(d) State, with justification, which of the two athletes should be selected. (NEAB)