Bacterial pneumonia attacks a dogs immune system causing it to fail. It is estimated that between 2 and 25 percent of the global domestic dog population is infected with the virus. Bacterial pneumonia is primarily transmitted from dog to dog through biting.

A one-step pulse test has been developed for the detection of bacterial antibodies. It is estimated that 94.7% of dogs with bacterial pneumonia test positive and 96.1% of dogs without bacterial pneumonia test negative using this test. Assume that 5% of the local dog population is actually infected with bacterial pneumonia.

Use this information to answer the following:

(a) For a population of 100 000 dogs:

(i) how many are estimated to be infected with bacterial pneumonia?

(ii) how many of the dogs in (a)(i) will test positive?

(b) Use your answers from (a) to help construct a 2 * 2 table of counts displaying the results for this sample. Complete the table.

(c) Estimate the proportion of local dogs that would test negative for bacterial pneumonia but actually be infected with bacterial pneumonia?