Elementary Statistics Question 6 (For question 6, just write down the answer. No explanation is needed.) (a) In the calculation of which of the following summary statistics, all the data in the data set are used? (you may choose one or more than one answer) I: Range, II: Interquartile range, III: Standard deviation. (2 marks) (b) The number of hours of sleep during Sunday for a college student is known to be a right-skewed distribution. For the first quartile is 5.8 hours and median is 6.6 hours, which of the following could be the third quartile? I: 7.2 hours, II: 7.4 hour, or III: 8.2 hours. (2 marks) (c) Every package of Christmas chocolate set contains one pack of white chocolate and one pack of dark chocolate. The weight of a pack of white chocolate follows normal distribution with mean 250 grams and standard deviation 4 grams. The weight of a pack of dark chocolate follows another normal distribution with mean 300 grams and standard deviation o grams. The weight of white chocolate and the weight of dark chocolate are independent. By using T to denote the total weight of chocolate in a package, it is known that the mean of T is 550 grams and standard deviation of T is 8.0623 grams. Find the value of a. (2 marks) (d) In a factory, estimation of the population mean amount of oil in a bottle are performed regularly. The amount of oil in a bottle is normally distributed with population standard deviation of 0.2 mL. For the point estimate should be within + 0.03 mL from the true population mean at the 99% confidence level, find the smallest sample size. (4 marks) (Total: 10 marks)