There is an 88% chance that a Dumbo battery is not faulty.Dean orders 300 triple packs of Dumbo batteries for his shop.Find an estimate for the number of pack that contain exactly 2 faulty batteries...
I m thinking about 36 but I m not sure.
To find an estimate for the number of packs that contain exactly 2 faulty batteries, we can use the concept of probability.
First, let's find the probability that a single pack contains exactly 2 faulty batteries. Given that there is an 88% chance that a Dumbo battery is not faulty, the probability that a single battery is faulty is 1 - 0.88 = 0.12.
To find the probability of exactly 2 faulty batteries in a single pack, we can use the binomial probability formula: P(x) = nCx * p^x * (1-p)^(n-x), where n is the total number of batteries in a pack, x is the number of faulty batteries, and p is the probability of a single battery being faulty. In this case, n = 3, x = 2, and p = 0.12.
P(2 faulty batteries in a single pack) = 3C2 * 0.12^2 * (1-0.12)^(3-2)
= 3 * 0.12^2 * 0.88^1
= 0.317952
Now, to estimate the number of packs that contain exactly 2 faulty batteries out of the 300 triple packs ordered by Dean, we can multiply the probability of 2 faulty batteries in a single pack by the total number of packs:
Estimated number of packs = 0.317952 * 300
≈ 95.39
Therefore, the estimate for the number of packs that contain exactly 2 faulty batteries is approximately 95.39. Based on this estimate, 36 seems to be a reasonable estimate but might be slightly lower than the actual value.