Use the given variances and the central eighty percent

Oil volumes in Small, Regular and Large bottles are normal.

Bottle	Mean (ml)	Variance (ml²)
Small	610	25
Regular	1050	$\sigma^2$
Large	1200	50

(i) Explain why Small volume can be modelled as normal although oil volume cannot be negative.1 mark

(ii) Three Small bottles are randomly chosen. Find the probability that one contains more than 615 ml and the other two less than 602 ml each.3 marks

(iii) Find σ if 80% of Regular bottles contain between 1040 and 1060 ml.3 marks

(iv) Find the probability that two random Large bottles contain more than four times the volume in one random Small bottle.3 marks

The source also prints “The mass of an empty bag is assumed to be negligible”; this unrelated bag note has no role in the bottle-volume model.