maths exerciseto help with probability, Exercises of Mathematical Methods

Download maths exerciseto help with probability and more Exercises Mathematical Methods in PDF only on Docsity!

5a Binomial assumes a constant probability, but although the school is described as ‘large’ it is still finite, so drawing without replacement causes the probabilities to change. For example, suppose there are 500 students in the school; 75 travel by bus. If you randomly draw five students who travel by bus, then the probability that the 70 sixth student also uses the bus is [> = 14.1%, noticeably different from 15%. It may appear that you could also cite a lack of independence, in that (for example) siblings would be expected to have the same transport behaviour, or bus use might differ according to student age. However, since the sample was drawn randomly from the whole school, neither of these is a valid argument against independence within the sample. b Let X be the number of students in the sample who travel by bus. X-B (20, 0.15) in approximation P(X =5) = 0.103 (3 s.f.) GLet X be the total number of questions Sheila answers correctly. xB (3 3) a P(X =5)= 0.0931 (3 s.f.) b P(X > 5)=0.0273 (3 sf.)