Example 1:

A marketing company finds that 15% of people respond to the flyers that they mail out.

a) Compute the probability that exactly 3 people P(X=3) of out a sample of 20 respond to the flyers they receive.

i) Compute this value by hand showing all work on the worksheet provided.

ii) Use "R" to compute this value using the following code;

dbinom(3, 20, .15)

b) Compute the probability thatno more than3 people out of a sample of 20 respond to the flyers they receive.

ii) Compute this value by hand showing all work on the worksheet provided.

ii) Use "R" to compute this value using the following code:

pbinom(3, 20, .15)

c) Compute the probability thatat least3 people out of a sample of 20 respond to the flyers they receive.

i) Compute this value by hand showing all work on the worksheet provided.

ii) Use "R" to compute this value using the following code:

pbinom(2, 20, .15, lower.tail = FALSE)NOTE:You could also use1-pbinom(2, 20, .15)

Questions:

e) In part 'c', what does the command "lower.tail=FALSE" do?

f) Explain why the code chunk was not pbinom(3, 20, .15, lower.tail=FALSE) for P(x