A m'wer ALL questions. Question 1 [Total: 16 marks] Boxplot of Mark Statistics exam marks ofa class of [00 students were analyzed using boxplot as shown above. (i) (ii) (iii) 0") From the boxplot, estimate (visually) the following marks (correct to the nearest whole number): lowest, first quartile, median, third quartile, Interquartile range. (7.5 marks) Briey describe the shape of the marks distribution. (2.5 marks) By referring to the median, give a possible value for the mean. (2 marks) In this case, which of them is considered more representative of the central tendency, median or mean? Explain. (2 marks) By evaluating the shape of the distribution, comment on the toughness of that Statistics exam, choosing from: easy, average, difcult. Give one reason for your choice, (2 marks) Question 2 [Total: 16 marks] The mean number of bacteria per ml of a liquid is known to be 4. Assuming that the number of bacteria follows a Poisson distribution, find the probability that (i) In 3 ml of liquid , there will be less than 2 bacteria. (6 marks) (ii) In 1 ml of liquid, there will be less than 3 bacteria (4 marks) (iii) In 0.5 ml of liquid, there will be more than 3 bacteria (6 marks)Question 3 [Total: 16 marks] The Accounting examination grade distribution for 3 age groups of students is as shown below: Frequency distribution table Grade Age Group Fail Pass Merit Distinction High Distinction (F) (P (M) (D (HD) Youth (Y) 5 21 12 14 6 Senior (S) 6 22 14 14 5 Old (0) 4 24 16 10 5 If a student is randomly chosen: (1) What is the probability he/she had a HD grade? (2 marks) (ii) What is the probability of he/she getting a HD grade given that he/she was from Y group? (3 marks) (iii) What is the probability he/she was from O group? (2 marks) (iv) What is the probability he/she received a D grade and was from Y group? (2 marks) (v) What is the probability he/she was from O group and received a F grade? (2 marks) (vi) What is the probability of his/her grade being M given he/she was from S group? (3 marks) (vii) What is the probability of his/her grade being M or higher? (2 marks)Question 4 [Total: 16 marks] (a) Mary bought 20 electric bulbs from a large scale second hand good dealer who didn't allow testing. Historical records show that 25% of the bulbs are spoilt. Find the probability that she will get: i) No spoilt bulb. (3 marks) (ii) Exactly two spoilt bulb. (3 marks) (iii) 20 spoilt bulbs. (3 marks) (iv) More than 3 spoilt bulbs. (3 marks) (b) Classify each of the following as quantitative or qualitative variable. Hence classify also the level of measurements (nominal-level, ordinal-level, interval-level, or ratio-level of measurement). (4 marks) i) Type of sport's games in University ii) Number of household which the annual income more than RM50,000. iii) Student ID number of foreign students in a statistics class iv) Rankings of Wai Kee in a class 8Question 5 [Total: 16 marks] The time taken by the customers of company to settle invoices is normally distributed with mean 20 and variance 16 days. A discount is given for every invoice which is settled in less than 12 days (a) Find the probability that an invoice is settled in more than 12 days (3 marks) (b) Find the probability that an invoice is settled in 20 to 26 days (4 marks) (c) Determine, out of 500 invoices, the expected number of invoices which are given discounts. (4 marks) ((1) Find the probability that at most 4 out of 10 invoices are given discounts. (5 marks) END OF QUESTIONS 10