Pearson Edexcel Level 3 GCE Mathematics

. The number of bacteria, n thousand per cm3 , in a sample of liquid is measured over a period of time, t, in hours. The data is shown in the table. t 3.9 5.5 6.8 8.5 10.6 11.5 13.3 14.7 16.5 17.8 n 10. 1 13.1 14.6 20.7 27.9 31.5 40 49.9 64.7 75.6 The data is coded using the changes of variable x = t and y = log10 n. The regression line of y on x is found to be y = 0.7606 + 0.0635x. (a) Given that the data can be modelled by an equation of the form n = abt where a and b are constants, find the values of a and b. (3) (b) Give an interpretation of the constant a in this equation. (1) (c) Explain why this model is not reliable for estimating the number of bacteria after 24 hours. (1) (Total 5 marks) _____________________________________________________________________________ 2 2. In a factory, three machinists, Amy, Brad and Ceri, are used to sew shirts. Amy sews 40% of the shirts. Brad sews 35% of the shirts. Ceri sews the rest of the shirts. It is known that 5% of the shirts sewn by Amy are faulty, 2% of the shirts sewn by Brad are faulty and 3% of the shirts sewn by Ceri are faulty. (a) Draw a tree diagram to illustrate all the possible outcomes and associated probabilities. (3) A shirt is selected at random. (b) Calculate the probability that the shirt is sewn by Brad and is not faulty. (2) (c) Calculate the probability that the shirt is faulty. (2) (d) Given that the shirt is faulty, find the probability that it was not sewn by Ceri. (3) (Total 10 marks) _________________