Keep the instructed rounded model consistent with later probabilities

State the parameters of every normal distribution used. Grapefruits and papayas are sold by mass. The table gives mean mass, standard deviation (SD) and price in dollars per gram.

Fruit	Mean (g)	SD (g)	Price / g
Grapefruit	μ	15	0.007
Papaya	450	20	0.008

(i) Given 65% of grapefruits weigh more than 300 g, show that μ=306 to the nearest whole number.2 marks

Take μ=306 for the remaining parts.

(ii) Find the probability that 3 random grapefruits have total mass below 950 g.2 marks

(iii) Ten grapefruits are randomly chosen. Find the probability that more than half weigh over 300 g.2 marks

(iv) Find the probability that the total mass of 3 random grapefruits differs from that of 2 random papayas by at most 100 g.3 marks

(v) Find the probability that 4 grapefruits cost at least 9 dollars.3 marks

(vi) A promotion offers one grapefruit and one papaya for a fixed price. Find the least price a dollars giving at least 90% probability of not making a loss.3 marks