A supplier of company X makes on an average of 5 defective pieces. The company accepts a sample if there are no more than 7 defective pieces. What are the chances that the company will reject the sample?
To find the chances that the company will reject the sample, we need to calculate the probability of having more than 7 defective pieces in the sample.
To do this, we can use the binomial distribution formula. The formula for the probability of having exactly k successes in n independent Bernoulli trials is:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Where:
- n is the number of trials
- k is the number of successful outcomes
- p is the probability of success for each trial
- (nCk) is the binomial coefficient, also known as "n choose k"
In this case, we want to find the probability of having more than 7 defective pieces, which means calculating the probability for k = 8, 9, 10, 11, and so on.
However, we don't know the total number of trials, which is required for the binomial distribution formula. Therefore, we need to make an assumption or estimate about the sample size.
Let's say we assume a sample size of 100 pieces from the supplier. We can then calculate the probability of having more than 7 defective pieces using this assumption.
P(X > 7) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)]
To calculate each individual probability, you can substitute the values into the binomial distribution formula using the values:
- n = 100
- k (number of defective pieces) = 0, 1, 2, ..., 7
- p (probability of defective piece) = 5 defective pieces out of total 100 (5/100 = 0.05)
Once you have calculated the probabilities for k = 0 to 7, you can sum them up and subtract the result from 1 to find the probability of having more than 7 defective pieces and therefore the chances of the company rejecting the sample.