A company sells seeds and claims that \(55 \%\) of its pea seeds germinate.
Write down a reason why the company should not justify their claim by testing all the pea seeds they produce.
A random selection of the pea seeds is planted in 10 trays with 24 seeds in each tray.
Assuming that the company's claim is correct, calculate the probability that in at least half of the trays 15 or more of the seeds germinate.
Write down two conditions under which the normal distribution may be used as an approximation to the binomial distribution.
A random sample of 240 pea seeds was planted and 150 of these seeds germinated.
Assuming that the company's claim is correct, use a normal approximation to find the probability that at least 150 pea seeds germinate.
Using your answer to part (d), comment on whether or not the proportion of the company's pea seeds that germinate is different from the company's claim of \(55 \%\)