Question

Suppose that 20% of coffee drinkers have their morning cup of coffee at home (as opposed to having it outside home). A random sample of 20 coffee drinkers is randomly selected. Suppose you have verified this is a Binomial experiment.

1-Identify the number of individual trials.

2-Define the binomial random variable X, in the context of question.

3-What is the probability that exactly 4 of the 20 randomly selected coffee drinkers have their morning cup of coffee at home?

4-What is the probability that at least three of the 20 randomly selected coffee drinkers have their morning cup of coffee at home?

Answer 1

Q1) The number of individuals trials here are given as the random sample size of coffee drinkers here. Therefore 20 is the number of individual trials here.

Q2) The number of coffee drinkers who have their coffee at home is modelled here as:

Q3) The probability that exactly 4 of the 20 randomly selected coffee drinkers have their morning cup of coffee at home is computed using the binomial probability function as:

Therefore 0.2182 is the required probability here.

d) The probability that at least three of the 20 randomly selected coffee drinkers have their morning cup of coffee at home is computed here as:

P(X >= 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)

Therefore 0.7939 is the required probability here.