Question

In average, the probability that an individual employee commutes to work by car is 0.65. If 20 employees are selected as the sample:

(What type of distribution is this i.e. Gaussian, Poisson, etc.)

1. What is the probability that all the 20 employees do NOT commute by car? Calculate by hand.
2. What is the average number of employee who commute to work by car? Calculate by hand.

Answer 1

This is an example of the Binomial Distribution.

Let be the random variable denoting the number of employees that commute to work by car.

As per the given information, the probability of that the employee commutes to the work by a car is .

Here, the sample size is .

Therefore, follows distribution.

(a)

The probability that none of the employees travel by car is:

(b)

The average nimber of employees commuting to work by car is: