a. A petrol station finds that its daily sales, in litres, are normally distributed with mean 4520 and standard deviation 560.

i. Find on how many days of the year (365 days) the daily sales can be expected to exceed 3900 litres.

The daily sales at another petrol station are X litres, where X is normally distributed with mean m and standard deviation 560. It is given that P(X > 8000) = 0.122.

ii. Find the value of m.

iii. Find the probability that daily sales at this petrol station exceed 8000 litres on fewer than 2 of 6 randomly chosen days.

b. The random variable Y is normally distributed with mean μ and standard deviation σ. Given that σ = 2/3 μ, find the probability that a random value of Y is less than 2μ.