Problem 1

Suppose 65% of Princeton students like World Coffee better than Hoagie Haven. We selected a random sample of 20 students, and asked them which they prefer. What is the probability that more than 18 students said “World Coffee”? Write R code to compute the actual probability.

Hint:

We solved a very similar problem in class on April 2 with coin tosses. Each student answer can be thought of as being like a coin toss. Decide whether you want “Heads” to represent HH or WC, and then solve the problem using pbinom, just like we did in class.

Problem 2

In class, we saw several ways to compute the cumulative probability for the binomial distribution: we used pbinom; we summed up the outputs of dbinom; we also generated a large sample using rbinom, and then computed the proportion of the generated numbers that was under a certain threshold.

Part 2(a)

Write a function named MyPbinom1, which works just like pbinom. You may use dbinom but not rbinom in the function you write.

Part 2(b)

Write a function named MyPbinom2, which works just like pbinom. You may use rbinom but not dbinom in the function you write.