Final answer:
To find the probability that at most two boxes weigh less than 6.0171 pounds each, you can use the binomial probability formula. By assuming equal probability for all boxes, you can calculate the probability of having zero, one, or two boxes weighing less than 6.0171 pounds. The probability that at most two boxes weigh less than 6.0171 pounds is approximately 0.937.
Step-by-step explanation:
To find the probability that at most two boxes weigh less than 6.0171 pounds each, we can use the binomial probability formula. Let's define the success as a box weighing less than 6.0171 pounds. If y is the number of boxes that weigh less than 6.0171 pounds, we want to find P(y ≤ 2). To calculate this probability, we can use the binomial probability formula:
P(y ≤ 2) = P(y = 0) + P(y = 1) + P(y = 2)
Now we can substitute the values into the formula. Since we don't have any specific information about the probability of a box weighing less than 6.0171 pounds, we'll assume equal probability for all boxes. Let's say there are a total of n boxes. Then the probability of a box weighing less than 6.0171 pounds is 2/9 (since we want to find at most two boxes, and the probability of each box being less than 6.0171 pounds is 2/9).
Using the binomial probability formula, we have: P(y = 0) = (2/9)^0 * (7/9)^9 = (7/9)^9 ≈ 0.263
P(y = 1) = 9C1 * (2/9)^1 * (7/9)^8 = 9 * 2/9 * (7/9)^8 ≈ 0.395
P(y = 2) = 9C2 * (2/9)^2 * (7/9)^7 = 9 * 8/2 * (2/9)^2 * (7/9)^7 ≈ 0.279
Finally, we can calculate the probability:
P(y ≤ 2) = P(y = 0) + P(y = 1) + P(y = 2)
P(y ≤ 2) ≈ 0.263 + 0.395 + 0.279 ≈ 0.937