Answer:
Binomial distribution could be used to model the number of failed drawers from the sample of 10.
Step-by-step explanation:
We are given the following information:
We treat drawers fail the easy slide test as a success.
P(drawers fail the easy slide test) = 2% = 0.02
The chance of failure is independent between drawers.
A manufacturer samples 10 drawers from a batch.
Since,
- The experiment consists of 10 repeated trials.
- Each trial can result in just two possible outcomes - drawers fail the easy slide test or drawer passes the easy slide test.
- The chance of failure is independent between drawers.
Then the number of drawers that fail the easy slide test follows a binomial distribution, where
![P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%3D%20%5Cbinom%7Bn%7D%7Bx%7D.p%5Ex.%281-p%29%5E%7Bn-x%7D)
where n is the total number of trails, x is the number of success, p is the probability of success.
Here, the parameters of binomial distribution are
n = 10, x = number of failed drawers(discrete values, x = 0, 1,...,10), p = 0.02
![P(X=x) = \binom{10}{x}(0.02)^x.(0.98)^{10-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%3D%20%5Cbinom%7B10%7D%7Bx%7D%280.02%29%5Ex.%280.98%29%5E%7B10-x%7D)