Let X be the number of defect bottles from an operation of manufacturing watcr bottles in a carton of 24 bottles. A total of 40 cartons are inspected and the number of defect bottles for each carton are recorded in Table 2. Table 2 Number of defects \"n\" Probablll 0.0080 0.0960 0.3 840 0.5120 i) Find the value of M. [2 Marks] ii) Can we conclude that the number of defect bottles recorded fit to the Binomial distribution at 1% signicance level with n = 3 and p = 0.2? [10 Marks] CONFIDENTIAL 21221UBUM2413 QUESTION 7 [14 Marks] A study is conducted to determine the relationship between the results (pass or fail) in a mathematics course among UMP students and their education background (STPM, Matriculation and Diploma program). A random sample of 75 UMP students were observed where the ratio of passed and failed students is 2:1. Table 3 shows the distribution of passed and failed students from three different education backgrounds. Table 3 Education Results of mathematics course at UMP back_round STPM __ i) Find the value of X and Y. [4 Marks] ii) Would you conclude that the results of UMP students in mathematics course is dependent on their education background at a = 0.025? [10 Marks]