State which distribution (joint, marginal, conditional) is best used to answer t

Question

State which distribution (joint, marginal, conditional) is best used to answer the question and then give the answer.

1. On a particular day, what is the probability that there are 5 technicians working and that the average number of hours produced per technician is at least 8?

2. On a particular day, what is the probability that the average number of hours produced per technician is less than 8.

3. If there are 6 technicians working on a particular day, what is the probability that the average number of hours produced per technician is less than 8?

4. On a particular day, what is the probability that fewer than 6 technicians are working?

Explanation / Answer

1. This probability will give intersection between technician working and hours produced hence joint distribution.

2. Here no condition or intersection single event so marginal distribution.

3. Here condition is put on technician so conditional distribution.

4. Same as 2 marginal distribution.

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