A paper manufacturer claims that fewer than 1 in 100 of its reels (2 ton rolls) of paper is flawed. A customer has just received a large shipment of these reels and proceeds to check a random sample of 600 of them for flaws. Of this sample, 14 reels are found to be flawed. What is the probability of finding at least 14 flawed reels in this sample?
Part 2
What would u conclude about the manufacturers claim?
The claim is probably true?
The claim may be false?
The claim is probably false?
Since the probability is very small of finding at least 14 reels in the sample (see previous post), you can conclude that the claim is probably true.
To calculate the probability of finding at least 14 flawed reels in this sample, we can use the binomial distribution formula. The binomial distribution is used when we have a fixed number of independent trials, where each trial has only two possible outcomes (in this case, flawed or not flawed), and the probability of success (finding a flawed reel) remains the same for each trial.
Let's denote the probability of finding a flawed reel as "p". The manufacturer claims that fewer than 1 in 100 of its reels is flawed, which means p is less than or equal to 0.01 in this case.
The probability of finding exactly k flawed reels in a sample of size n can be calculated using the binomial distribution formula:
P(X = k) = (n C k) * p^k * (1 - p)^(n - k)
where (n C k) represents the number of ways to choose k objects out of a set of n objects, and p^k * (1 - p)^(n - k) represents the probability of getting k successes and (n - k) failures.
In this case, we want to find the probability of finding at least 14 flawed reels, which means we need to calculate the cumulative probability of finding 14 or more flawed reels:
P(X >= 14) = P(X = 14) + P(X = 15) + ...
We can use a tool like a binomial calculator or statistical software to calculate this probability directly. For example, using the binomial calculator on a website like stattrek.com, you can input the values n = 600, p = 0.01, and calculate the cumulative probability P(X >= 14). The result will be a very small number.
With this information, we can conclude that the probability of finding at least 14 flawed reels in this sample is very small. Therefore, we can infer that the manufacturer's claim of fewer than 1 in 100 of its reels being flawed is probably true.