The battery in Sue’s phone runs out at random moments. Over a long period, she has found that the battery runs out, on average, 3.3 times in a 30-day period.
(i) Find the probability that the battery runs out fewer than 3 times in a 25-day period. 
(ii) (a) Use an approximating distribution to find the probability that the battery runs out more than 50 times in a year (365 days). 
(b) Justify the approximating distribution used in part (ii) (a). 
(iii) Independently of her phone battery, Sue’s computer battery also runs out at random moments. On average, it runs out twice in a 15-day period. Find the probability that the total number of times that her phone battery and her computer battery run out in a 10-day period is at least 4.