The weight, of a particular type of melon sold in a supermarket follows a normal distribution with mean 1.8 kg and standard deviation 0.2 kg, that is, ~(1.8, (0.2)²).

Answer all the following questions. Give your final numerical answers correct to 2 decimal places, unless otherwise stated.

What is the probability that a randomly chosen melon has a weight

A) less than 1.6 kg, i.e. ( < 1.6), [2 marks]

B) at least 1.9 kg, i.e. ( 1.9), [2 marks]

C) between 1.5 kg and 2 kg, i.e. (1.5 < < 2). [2 marks]

The melons are sold by weight at a price of $3 per kg. Let denote the price of a randomly chosen melon, i.e = 3

D) Calculate the mean of the distribution of . [2 marks]

F) Calculate the variance of the distribution of . [2 marks]