- [Maximum mark: 7]
The records at a driving school show that 55 % of students pass their driving test on the first attempt.
A group of 20 students take their driving test for the first time.
As part of its quality control, the driving school uses the model X ~ B(20, 0.55), where X is the number of students who pass the driving test.
(a) Calculate the
(i) mean of X [2]
(ii) variance of X. [2]
(b) Find the probability that
(i) exactly 14 students pass the test [2]
(ii) fewer than 5 students pass the test. [2]
(c) State one assumption that the driving school makes in using this model. [1]