Please help me with the following questions, I cannot solve that

Section B (84%) - Long Questions Answer ALL questions in this section in the answer script provided. Each question carries 12 marks. Question BI Consider the following stem and leaf display for a set of sample data. Stem Leaves (unit = 0.01) 0 19 56 21a89 3 23578 4 4569 5 239 (a) (i) Find the 1" Quartile (Q1) and 3"d Quartile (Q3) in terms of a and b. (2 marks) (ii) Suppose the inter-quartile range is 0.22 and the distances between the two quartiles and the median are the same (i.e. Q, - Median = Median -Q, ). Find the values of a and b. (2 marks) (b) Suppose there is at least 75% data within the interval ,\\' to Y. By using the Chebyshev's theorem, find the interval X to ) around the sample mean. (Correct your final answers to 3 decimal places) (4 marks) (c) Suppose a frequency table for the above data set is constructed with 5 classes. The smallest data value from the sample is used as the lower class limit of the first class. Calculate the mean and variance of the grouped data using the frequency table. (Correct your final answers to 3 decimal places) (4 marks) Question B2 (a) The table below shows the discrete probability distribution of a random variable .I 18 25 P(X) 0.2 0. 1 Suppose / = 12. Find the values of w' and A. Hence. find the variance. (5 marks) (b) Suppose 15 students in a class are to be assigned randomly into $ groups for group presentation. Each group contains 3 students. In how many different ways can these groups be formed? (3 marks) (c) Suppose 5 cards are randomly drawn from an ordinary deck of playing $2 cards one-by- one without replacement. Find the probability of getting at most one Ace card. (Correct your final answer to I decimal places) (+ marks) CS Additional Assign ment camec Page 3 of 7 CamScannerSection B (84%) - Long Questions Answer ALL questions in this section in the answer script provided. Each question carries 12 marks. Question BI Consider the following stem and leaf display for a set of sample data. Stem Leaves (unit = 0.01) 0 19 56 21a89 3 23578 4 4569 5 239 (a) (i) Find the 1" Quartile (Q1) and 3"d Quartile (Q3) in terms of a and b. (2 marks) (ii) Suppose the inter-quartile range is 0.22 and the distances between the two quartiles and the median are the same (i.e. Q, - Median = Median -Q, ). Find the values of a and b. (2 marks) (b) Suppose there is at least 75% data within the interval ,\\' to Y. By using the Chebyshev's theorem, find the interval X to ) around the sample mean. (Correct your final answers to 3 decimal places) (4 marks) (c) Suppose a frequency table for the above data set is constructed with 5 classes. The smallest data value from the sample is used as the lower class limit of the first class. Calculate the mean and variance of the grouped data using the frequency table. (Correct your final answers to 3 decimal places) (4 marks) Question B2 (a) The table below shows the discrete probability distribution of a random variable .I 18 25 P(X) 0.2 0. 1 Suppose / = 12. Find the values of w' and A. Hence. find the variance. (5 marks) (b) Suppose 15 students in a class are to be assigned randomly into $ groups for group presentation. Each group contains 3 students. In how many different ways can these groups be formed? (3 marks) (c) Suppose 5 cards are randomly drawn from an ordinary deck of playing $2 cards one-by- one without replacement. Find the probability of getting at most one Ace card. (Correct your final answer to I decimal places) (+ marks) CS Additional Assign ment camec Page 3 of 7 CamScanner