The weight of a package delivered by a courier company is normally distributed with mean 15 kg and standard deviation 1.75 kg.

(a) There are 9% of the packages weigh heavier than w kg. Find the value of w. (4 marks)

(b) Suppose the shipping fee set by the courier company is $150 basic charge, together with an additional charge of $16 per kg of the package. Find the following summary statistics of the shipping fee:

(I) Mean

(II) Standard deviation

(III) Variance

(IV) Median

(V) 91st percentile