CAIE FP2 2009 November — Question 9

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2009
SessionNovember
TopicChi-squared distribution

9 It has been found that \(60 \%\) of the computer chips produced in a factory are faulty. As part of quality control, 100 samples of 4 chips are selected at random, and each chip is tested. The number of faulty chips in each sample is recorded, with the results given in the following table.
Number of faulty chips01234
Number of samples212274910
The expected values for a binomial distribution with parameters \(n = 4\) and \(p = 0.6\) are given in the following table.
Number of faulty chips01234
Expected value2.5615.3634.5634.5612.96
Show how the expected value 34.56 corresponding to 2 faulty chips is obtained. Carry out a goodness of fit test at the 5\% significance level, and state what can be deduced from the outcome of the test.