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Question 1 [20 marlce] (a) The following data represent the price (in sen) of 100 grams of red chillies in the local market for 20 consecutive days. 32 81 BO 85 95 33 35 82 77 30 76 74 87 88 85 81 90 92 90 88 (i) Compute the measurement of central tendency. (6 marks) (ii) Compute the variance and standard deviation. (6 marks) (b) The causes for late on different occasions. Causes for Late Arrival Number of Occasions Family problems 8 Had to take the bus 4 Woke up late 20 Bad weather 3 Sick 6 Traffic tied-up 32 Make a pareto chart for these data. (3 marks) Question 2 [20 marks] (a) The probability that boards purchased by a cabinet manufacturer are unusable for building cabinets is 0.15. The cabinet manufacturer bought Iil'teen boards. Find the probability that (i) none of the fifteen boards are unusable for building cabinets. (3 marks) (ii) at most two of the lifteen boards are unusable for building cabinets. (5 marks) (b) An average of five calls for service per hour are received by a technician. In a randomly selected hour, find the probability that (i) exactly two calls for service will be received. (3 marks) (ii) more than one call for service will be received. (5 marks) Page 2 of 7 CITY UNIVERSITY Date : 29'" April 2021 Course : BBQT2013 Business Statistics (c) At a certain community college. the time that is required by students to complete the mathematics competency examination is normally distributed with a mean of 57.3 minutes and a standard deviation of 8 minutes. Find the probability that a student takes between 56 minutes and 1 hourto complete the examination. (4 marks) Question 3 [20 marks] (a) The mean wage for all 5000 employees who work at a large company is RM21.50 per hour and the standard deviation is RM3.50 per hour. Let f be the mean wage per hour for a random sample of certain employees selected from this company. Find the mean and standard deviation of 2 for a sample size of 150. (3 marks) (b) A sample of 1500 homes sold recently in a state gave the mean price at homes equal to RM344,750. The population standard deviation of the prices of homes in this state is RM63.150. Construct a 99% confidence interval for the mean price of all homes in this state. (7 marks) (c) A random sample of eleven packages was selected from a machine packaging sugar in packages marked 1kg. The actual weights of sugar in kg were: 1.01 1.05 1.03 1.07 0.98 0.99 1.04 1.01 1.05 0.99 1.04 Assuming that the weights are normally distributed, calculate a 95% confidence interval for the mean weight of sugar in packages marked 1kg. (1 0 marks)
