A factory produces components of which \(1 \%\) are defective. The components are packed in boxes of 10 . A box is selected at random.
Find the probability that the box contains exactly one defective component.
Find the probability that there are at least 2 defective components in the box.
Using a suitable approximation, find the probability that a batch of 250 components contains between 1 and 4 (inclusive) defective components.
A web server is visited on weekdays, at a rate of 7 visits per minute. In a random one minute on a Saturday the web server is visited 10 times.
Test, at the \(10 \%\) level of significance, whether or not there is evidence that the rate of visits is greater on a Saturday than on weekdays. State your hypotheses clearly.
State the minimum number of visits required to obtain a significant result.
State an assumption that has been made about the visits to the server.
In a random two minute period on a Saturday the web server is visited 20 times.
Using a suitable approximation, test at the \(10 \%\) level of significance, whether or not the rate of visits is greater on a Saturday.