Suppose that the 1st quartile Q1 of the sample data is 53 and the interquartile range of the sample data is 23

The AMS1303 final marks of 21 students were recorded and the sample data are shown in the following stem-and-leaf plot. Stem (in 10) Leaf (in 1) UVIVIAN 00 00 (a) Suppose that the 1" quartile Q1 of the sample data is 53 and the interquartile range of the sample data is 23. Find A and B. (b) Compute the mean, median, mode and standard deviation of the marks of 21 students. (c) Construct a box-and-whisker diagram for the above data. (d) An additional data X22 is added, and the sample mean increases by 1, what is the sample standard deviation? 2. (a) In a sample of 100 BBA students, 40 take AMS1303, 40 take FIN1001, 20 take GEN1000. Twenty five percent of those taking AMS1303 also take FIN1001; thirty percent of those taking FIN1001 also take GEN1000; and fifty percent of those taking GEN 1000 also take AMS1303. In addition, 3 of them take all three subjects. Suppose that a student is randomly chosen from this sample. (i) Find the probability that the chosen student takes AMS1303 only. (ii) Given that the student takes FIN1001, what is the probability that he/she is not taking AMS1303? (iii) Find the probability that the chosen student takes AMS1303 or GEN1000. (b) A store sells three brands of mobile phones - Brands, A, S, and H. Twenty five percent of mobile phones are from Brand S. Suppose that x% of mobile phones are defective. In addition, twenty five percent and thirty percent of defective mobile phones are from Brands A and H, respectively. Twenty percent and twenty five percent of non-defective mobile phones are from Brands S and H, respectively. Find x. In addition, if one mobile phone of Brand A is randomly chosen, what is the chance that the mobile phone is non- defective