Question

16. Determine whether the given procedure results in binomial distribution. Explain your answer using the 4 requirements for a binomial distribution. You have to be specific in answering these, and not just listing the requirements.

a. Record the temperature of 863 people entering the State of Secretary office this week.

b. Asking 50 senators in the current Congress with replacement whether he or she is in favor of detention camps for children at the Southern border.

c. Asking all that attending the Zoom meeting earlier today whether they watch “The Bachelor”.

d. Asking each student in this class (all 30 of them) whether they are going to vote in November.

Answer 1

The 4 requirements for a binomial distribution

Requirement 1: The experiment consists of n identical trials

Requirement 2: Each trial results in one of two outcomes, called success and failure

Requirement 3: The probability of success = p remains the same from trial to trial

Requirement 4: The n trials are independent.

(a)

The given procedure does not result in binomial distribution because Requirement 2: is not satisfied since we are just recording the temperature of 863 people entering the State of Secretary office this week.

(b)

The given procedure results in binomial distribution because all the 4 requirements as follows:

Requirement 1: The experiment consists of n identical trials. Here n = 50, fixed.

Requirement 2: Each trial results in one of two outcomes, called success and failure. Here, whether he or she is in favor of detention camps for children at the Southern border.

Requirement 3: The probability of success = p remains the same from trial to trial. Here p = Probability of favor of detention camps for children at the Southern border.

Requirement 4: The n trials are independent. Here the senetors are independent of each other.

(c)

The given procedure results in binomial distribution because all the 4 requirements as follows:

Requirement 1: The experiment consists of n identical trials. Here n = all that attending the Zoom meeting earlier today , fixed.

Requirement 2: Each trial results in one of two outcomes, called success and failure. Here, whether they watch “The Bachelor”.

Requirement 3: The probability of success = p remains the same from trial to trial. Here p = Probability of whether they watch “The Bachelor”.

Requirement 4: The n trials are independent. Here all that attending the Zoom meeting earlier today are independent of each other.

(d)

The given procedure results in binomial distribution because all the 4 requirements as follows:

Requirement 1: The experiment consists of n identical trials. Here n = 30, fixed.

Requirement 2: Each trial results in one of two outcomes, called success and failure. Here, whether they are going to vote in November.

Requirement 3: The probability of success = p remains the same from trial to trial. Here p = Probability of whether they are going to vote in November.

Requirement 4: The n trials are independent. Here all 30 students of the class are independent of each other.