3 (Total: 20 marks) Based on a recent study, the household utility bills for three-room flats in Singapore can be assumed to be normally distributed with mean $125 and standard deviation $38. a) If a household is randomly selected, i. What is the probability that its utility bill is more than $155? (3 marks) ii. What is the probability that its utility bill is between $102 and $133? (4 marks) iii. If 20% of the households utility bills are above a certain value V, find the value of V. (5 marks) b) Ten households were randomly selected for interview. What is the probability that the mean household utility bill is between $114 and $131? (8 marks)