(You do not have to do all four, but should do parts (a), (b), (c) for at least one of the four experiments -- and please don't all choose to do the same one!)
2. In Mendel's other experiment with the 600 red-flowering plants:
(a) If the true type of the parent is RW, what is the probability that
there are no white-flowering seedlings among 10 offspring?
(b) Does the Poisson approximation provide a good approximation?
(c) Repeat (a) and (b), if instead he had observed 20 offspring of each
red-flowering parent plant.
(d) Repeat (a) and (b), for the case of 10 offspring, but for the
modified experiment in which each RW-type red-flowering parent plant
produces a white-flowering offspring with probability 1/2.
(e) Repeat (a) and (b), for the experiment of (d), but now with 20
offspring of each plant tested.
3. In Mendel's experiment with the 600 red-flowering plants,
due to his typing procedure,
the actual probability he would classify a plant as
type RR is
p = (1/3) + (2/3)*(3/4)10 = 0.37 (why?)
In 600 parent plants, he classified 201 as RR. Use the Normal
approximation to find
(a) he would get a result this close to expectation, if p=1/3
(b) he would get a result this far from expectation, if p=0.37.
(p here is the probability the plant gets classified as RR: (a) is what
Mendel thought he should get, (b) is what he should actually have gotten.)
4. A better version of Question 2:
Out of 600 RW plants, what is the probability that exactly 0, 1, 10
are misclassified:
(a) if the probability of misclassification is (0.75)10
(b) the Poisson approximation to the values in (a)
(c) if the probability of misclassification is (0.5)10
(d) the Poisson approximation to the values in (c).
(Actually it should probably be 380 to 400 RW plants.)