Question:

(i) A soft drink machine is regulated so that it fills an average of 300 cL per cup. If the amount of drink in each cup is normally distributed with standard deviation equal to 25 cL, find the probability that a cup of drink chosen at random will contain

(a) between 290 cL and 310 cL,

(b) between 275 cL and 290 cL,

(c) less than 275 cL. (15 marks) of soft drink.

(ii) A certain product is put into cans by a canning machine. The mass of the product in a can has mean 22.40 kg and standard deviation 0.048 kg. A random sample of 36 cans is taken from this population; find the probability that the mean content of the sample falls between 22.41 kg and 22.42 kg. State any necessary assumptions you have made.

(iii) 75% of the houseowners in a particular area own a colour television set. Evaluate the probability that at least 73 of a random sample of 100 houseowners in the area own a colour television set.