8.1; Normal approximations: Mendel's experiments revisited

Back in section 2.4, we considered some of the results of Mendel's experiments. The general conclusion was that his results were "too close" to expectations. Now we can validate that idea, using the Normal approximation to a binomial.

In Mendel's first series of experiments, he was looking for a 3:1 segregation ratio. That is, the probability of the type of interest should be (under Mendel's theory) 3/4. He looked at a large number of plants, each of which should be, independently of the others, of the "dominant" type with probability 3/4, and the "recessive" type with probability 1/4.

Here is a summary of some of his results:

Trait       Number of seeds 
             or seedlings       Dominant type        Recessive type
=====================================================================
Seed shape        7324           Round   5474         Wrinkled 1850
Seed color        8023           Yellow  6022         Green    2001
Flower color       929           Red      705         White     224
Pod color          580           Green    428         Yellow    152  
=====================================================================

In another experiment, he had 600 red-flowering plants. Some of these (type RR) could produce only red offspring For the others (type RW) each offspring had probability 1/4 of bring white, 3/4 of being red. He believed (correctly) that 1/3 of the red-flowering parent plants were type RR, and 2/3 were type RW. He typed 10 offspring of each plant, and classified it as RR if it had only red offspring.
From his 600 parent plants, he ended up classifying 201 as type RR, and 399 as type RW.

An experiment he could have done, would be to cross his red-flowering plants with a white-flower one (type WW). In this case, the RR plants still produce only red-flowering offspring, but now the offspring of an RW type parent has white flowers with probability 1/2.