(a) [3 marks] Sugar is sold in bags of 1 kg. To ensure bags are not sold underweight, the machine is set to put a mean weight of 1004 g in each bag. The manufacturer claims that the process works to a standard deviation of 2.6 g. Calculate the proportion of bags manufactured that are not underweight. You are to assume the weights are Normally distributed. 1 (e) (b) [3 marks) Soap manufactured at a soap-making facility have a mean weight of 150 g and a standard deviation of 3 g. Fill in the blank showing how you obtain the answer: 7.67% of the bars of soap manufactured at this facility have weights less than g. You are to assume the weights are Normally distributed [3 marks] A machine produces bolts with mean length 4 mm and a standard deviation of 0.3 mm. Bolts are measured and any which are shorter than 3.5 mm or longer than 4.7 mm are rejected. Calculate the proportion of bolts that are rejected. You are to assume the lengths are Normally distributed. (d) [3 marks] The heights of people in the country Lilliput are Normally distributed with a mean of 89 cm and a standard deviation of 11 cm. Fill in the blank showing how you obtain your answer: 87% of people in Lilliput are over cm tall. The developmental process begins within an employee's first two or three days on the job. True False