1 Over a long period of time, \(20 \%\) of all bowls made by a particular manufacturer are imperfect and cannot be sold.
- Find the probability that fewer than 4 bowls from a random sample of 10 made by the manufacturer are imperfect.
The manufacturer introduces a new process for producing bowls. To test whether there has been an improvement, each of a random sample of 20 bowls made by the new process is examined. From this sample, 2 bowls are found to be imperfect.
- Show that this does not provide evidence, at the \(5 \%\) level of significance, of a reduction in the proportion of imperfect bowls. You should show your hypotheses and calculations clearly.