Question 1 Part A The weights (kg) of a random sample of ten students in a statistics class are as follows: 50 87 65 71 59 80 69 77 80 60 The following output, generated by the Microsoft Excel software is given: Summary Statistics Mean Standard Error 3.63 Median b Mode C Standard Deviation 11.48 Sample Variance d Kurtosis -0.71 Skewness -0.23 Range Minimum 50 Maximum 87 Sum 698 Count 10 i. Find the missing values a, b, c, d, and e. (5 marks) ii. Is the distribution of the weights skewed to the left or skewed to the right? Give two justifications to support your answer. (3 marks) iii. Using the values provided in the Excel output and the answers obtained in (i), state the values of X + 1.3s and X - 1.3s where X is the sample mean and $ is the sample standard deviation. (2 marks) iv. Using Chebyshev's theorem, calculate at least what percentage of the weights of this group of students are within the interval obtained in (iii). (2 marks) Part B A restaurant has found that 65% of the customers prefers to pay using c-wallet. i. Find the probability that exactly half of the 8 customers will pay their bills using e-wallet. (2 marks) ii. Find the probability that less than 3 of the 10 customers will pay their bills using e-wallet. (3 marks) ORM101 (May 2032 Semester. Take Home Examination) Page 3 iii. Find the probability that at least 3 of the 12 customers will not pay their bills using e-wallet. (4 marks) iv. Find the mean and standard deviation of the 14 customers will not pay their bills using e- wallet. (4 marks)