Question

Boxes of Product A are stacked on pallets that hold up to 500 lbs in a certain intermediate warehouse. The weight of the boxes follows a normal distribution with a mean of 5 lbs and a standard deviation of 0.5 lbs. Since the boxes weigh an average of 5 lbs and the pallet supports 500 lbs. In the company they determine that they can place 100 boxes per pallet, what do you think of this decision? Convincingly argue about your position (5 pts)

a) Assume that the pallets have a safety factor of 5 lbs. What is the probability that the total weight of 100 boxes exceeds 505 lbs?

b)How many boxes should we put on the pallet to ensure that the probability of exceeding the maximum weight of 500 lbs. is not greater than 0.1%?

c) If 15 boxes are selected at random,
What is the probability that the average weight of the boxes is less than 5 lbs?

What is the probability that the average weight of the boxes is below 4.8 lbs.?

Answer 1

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