Suppose that weekly household expenditures on petrol are normally distributed, with a mean of $120 and a standard deviation of $50.

i. A family is randomly selected. Find the probability that this family spends more than $245 per week on petrol?

ii. The government wants to promote public transport and will award a prize to the families who spend the lowest amount on petrol. If the government only wants to give a prize to 10% of households, what is the most that a family is allowed to spend on petrol each week to obtain the prize?

iii. In a sample of 25 families, what is the probability that the average weekly expenditure on petrol will be less than $105?