Question

According to a recent survey, an average worker is absent on nine days during the year for various reasons (e.g., illness, bereavement). Assuming 365 days in a year, 25 holidays, and ten bank holidays, the average worker has 230 working days per year.

Suppose that worker absenteeism is a good proxy for student absenteeism. Out of the 400 registered for an economics course in 2022, 32 students were absent from the final test.
Let X denote a random variable that captures the number of students taking economics absent on a given day. Provide an expression for the distribution of X.

Answer 1

The distribution of X, representing the number of absent students on a given day, can be described using a binomial distribution.

Step-by-step explanation:

The distribution of X, which represents the number of students absent on a given day, can be described using a binomial distribution.

The binomial distribution is appropriate when we have a fixed number of independent trials, with each trial having only two possible outcomes (in this case, absent or not absent).

To express this mathematically, we can use the formula:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Where:

• P(X=k) is the probability of exactly k students being absent
• n is the total number of trials (number of students registered for the course)
• k is the number of successful trials (number of absent students)
• p is the probability of a single trial being successful (probability of a student being absent on a day)

In this case, to find the distribution of X for the given data, we can use the values:

• n = 400 (number of registered students)
• p = 32/400 = 0.08 (probability of a student being absent on a day)

Using this information, we can calculate the probabilities for different values of X. For example, to find the probability of exactly 5 students being absent, we substitute n=400, k=5, and p=0.08 into the formula above.