QUESTION 1 The table below shows the weekly expenses (RM) of pupils at a school canteen in March 2018. a) b) Weekly expenses (RM) Number of pupils 0-5 8 5-10 13 10-15 28 15-20 41 20-25 10 Find the mean and variance for the above data. (5 marks) Draw a histogram to represent the above data. Hence, state the shape of the distribution. (5 marks) QUESTION 2 A survey found that most Malaysians purchase their airplane tickets either through online or from the ticketing centre. In this survey, 70% are Malays, 20.3% are Chinese and the remaining are from other ethnic groups. Among them, 51.2% Malays, 24.9% Chinese and 23.9% from other ethnic groups purchase airplane ticket online. a) b) c) d) Draw a tree diagram for the above study. (3 marks) Find the probability that a selected respondent purchases airplane ticket online. (2 marks) Calculate the probability that a selected respondent is from other ethnic groups and purchases airplane ticket online. (2 marks) Find the probability that a respondent is a Chinese, given that he or she purchases airplane ticket online. (3 marks) i Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL CS/DEC 2019/STA116 QUESTION 3 The probabilities that a traffic police officer will issue traffic summons during his work shift are given in the following table. a) b) Number of summons, X 0 1 2 3 4 Probability, P(X=x) 0.35 0.25 0.2 a 0.1 Show that the value of a is 0.1. Calculate i) P(X > 2). ii) Var(X). iii) E(X2 + 2X). (2 marks) (2 marks) (4 marks) (2 marks) QUESTION 4 A bank manager wants to study the number of customers who use the ATM located outside his office at midnight. On average, 1.5 customers walk up to the ATM and use it during any fifteen minutes interval at midnight. a) b) For a random midnight, find the probability that i) exactly two customers use the ATM during any fifteen minutes interval. ii) three or fewer customers use the ATM during any half an hour interval. (2 marks) (3 marks) By using an appropriate approximation, find the probability that at most twelve customers use the ATM during any four hours interval. (5 marks) © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL CS/DEC 2019/STA116 QUESTION 5 A continuous random variable X has the following probability density function fk(x-x2), 0