Question

A division of a company has over [200] employees,[48%] of which are male. the company is going to randomly select [10] of these employees to attend a conference. let [z=] the number of male employees chosen. is [z] a binomial variable? why or why not?

Answer 1

The variable z is a binomial variable in the given scenario.

Step-by-step explanation:

The random variable z represents the number of male employees chosen to attend the conference. In order for z to be a binomial variable, it must satisfy certain conditions:

1. The variable should have a fixed number of trials. In this case, the number of trials is 10, as the company is selecting 10 employees.
2. Each trial must be independent. This means that the selection of one employee does not affect the selection of another employee.
3. Each trial must have the same probability of success. In this case, the probability of selecting a male employee is fixed at 48% for each trial.
4. The trials must be mutually exclusive. This means that an employee can either be chosen or not chosen, but not both.

As the given scenario satisfies all these conditions, the variable z is indeed a binomial variable.

Answer 2

Yes, the random variable z is a binomial variable because it satisfies all the conditions for a binomial variable.

Step-by-step explanation:

Yes, the random variable z is a binomial variable. In order for a variable to be considered binomial, it must satisfy the following conditions:

1. There must be a fixed number of 10 trials. (z represents the number of male employees chosen out of 10.)
2. Each trial must be independent. (The selection of one employee does not affect the selection of another employee.)
3. There must be two possible outcomes for each trial: success or failure. In this case, a success is selecting a male employee, and a failure is selecting a female employee.
4. The probability of success must be the same for each trial. In this case, the probability of selecting a male employee is 48% and remains constant for each selection.

Since all the conditions are satisfied, the random variable

z

can be considered a binomial variable.