In one of Gregor Mendel's experiments he grew 929 pea plants of which 705 were purple-flowering.
Mendel's model was that each plant has chance 75% of being purple-flowering independently of other plants.
A Data 8 students simulates the following experiment 10,000 times:
O Count the number of successes in 929 i. i.d. success/failure trials each of which has success probability 0.75
Let X be the number of simulations in which the observed count of successes is at least 705.
1. In each part below, use a code cell to find numerical values that you can't easily find by hand.
a) Find the distribution of X. If it is one of the famous ones, just provide its name and parameters.
b) Find E(X).
c) Find SD(X).