On a particular day, 112 of 280 passengers on a particular DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding passes. In a random sample of eight passengers, use the binomial model to find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

Step-by-step explanation:

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:

Population of 280, which means that

112 use e-ticket check-in kiosk, which means that

Sample of eight passengers means that

Find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

This is P(X = 4). So

0.2348 = 23.48% probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

step-by-step explanation: