Question

Boxes of 6 ‑inch slate flooring tile contain 40 tiles per box. The count X is the number of cracked tiles in a box. You have noticed that most boxes contain no cracked tiles, but if there are cracked tiles in a box, then there are usually several.Does X have a binomial distribution?Yes. There are a fixed number of tiles per box, with a varying probabilitiy of success, p , and only two outcomes of interest (cracked or not cracked).No. The trials are not independent. If one tile in a box is cracked, there are likely more tiles cracked.There is not enough information to tell.Yes. There are a fixed number of tiles per box, with constant probability of success, p , and only two outcomes of interest (cracked or not cracked).

Answer 1

X is not a binomial distribution.

Explanation:

We are given the following in the question:

Number of tiles in every box = 40

The count X is the number of cracked tiles in a box.

We have to check whether X follows a binomial distribution or not.

Properties of binomial distribution:

• The experiment consist of n repeated independent trials.
• Each trial has two possible outcome either a success or a failure.
• The probability of success on each trial is same.

Conclusion:

• The distribution of X that are number of cracked tile in a box does not follow a binomial distribution because the probability of success for each trial is not same as the number of cracked tiles in each box can be different.
• The probability of getting a cracked tile is not constant in each box.