Spany sells seeds and claims that \(5 \%\) of its pansy seeds do not germinate. A packet of pansy seeds contains 20 seeds. Each seed germinates independently of the other seeds.
Find the probability that in a packet of Spany's pansy seeds
more than 2 but fewer than 5 seeds do not germinate,
more than 18 seeds germinate.
Jem buys 5 packets of Spany’s pansy seeds.
Calculate the probability that all of these packets contain more than 18 seeds that germinate.
Jem believes that Spany's claim is incorrect. She believes that the percentage of pansy seeds that do not germinate is greater than 5\%
Write down the hypotheses for a suitable test to examine Jem's belief.
Jem planted all of the 100 seeds she bought from Spany and found that 8 did not germinate.
Using a suitable approximation, carry out the test using a \(5 \%\) level of significance.