Chocolate boxes are labelled with a net weight of 500 g. The business selling the chocolate boxes fills the boxes to a net weight of 505 g, to avoid customer complaints. The weight of the chocolate boxes follows a normal distribution with a mean weight of 505 g and a standard deviation of 2.5 g.

(a) What is the probability that a box selected randomly will contain less than 500 g of chocolate?

2 (b) The business sets a target of less than 16% of all boxes will contain more than 510 g of chocolate. The business needs to change the mean weight of the boxes to meet this target. What is the mean weight required to meet the target if the standard deviation remains at 2.5 g?