Question 1 (20 marks) Mr. Simpson did a survey on all 10 students of his class to nd out the number of hours they spend on the intemet each day. and the data is recorded in hours as follows: m a) From the given set of data on the number of hours the students spend on the internet, compute the following: 0 Mean (2 marks) ii) Median (2 marks) iii) Mode (2 marks) iv) Range (2 marks) b) Calculate the variance and standard deviation for the number of hours the students spend on the internet. Show your working in table form. (5 marks) c) What is the 82rld percentile of this set of data? (2 marks) d) Find the Inter-Quartile Range of this data set. (5 marks) Kate is promoting the Royal Gold Foil Chiffon Cake in a supermarket. The probability of having different numbers of cakes sold each day is as shown in the probability distribution below: Number of cakes Probability sold 5 up to 10 0.14 10 up to 15 0.11 15 up to 20 0.27 20 up to 25 0.39 25 up to 30 0.09 a ) What is the expected number of cakes sold each day? (6 marks) b) If each cake costs $39.90, what is the expected sales (in dollars) in a week? (2 marks) c) Compute the standard deviation of the number of cakes sold. (6 marks) d) What is the probability that the number of cakes sold would be between 10 to 25 on any given day? (2 marks)The Human Resource department of the Singapore Pool Table Company took a sample of 7 blue-collar employees and collected the following data: b) d) Number of years working in the Salary (Y) company (X) (in $000's) 3.5 3.0 2.9 3.9 2.9 3.8 Using the least square method, construct a regression equation for estimating the salary of a blue collar worker, using number of years working in the company as a predictor. (8 marks) Compute the coefficient of correlation for the regression equation obtained in (a). Explain its signicance. (4 marks) By using the given attachment (with axes drawn), plot the data points in a scatter plot. Draw the line of best t. (6 marks) Estimate from the scatter plot, the salary of a blue-collar worker, if he has worked in the company for 7 years. (2 marks)