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A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 180 lb and a standard deviation of 43lb. The water taxi has a stated capacity of 25 ​passengers, and the water taxi was rated for a load limit of 3500 lb.

User Tisto
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Once upon a time in a land not so far away, there was a bright and sprightly water taxi. Let's call it 'HappiNess'. She was known far and wide for her distinct yellow hue, and her chirpy charm was the talk of the harbor. She carried people from one harbor to another with pride and style, and had quite a reputation for always being on time.

Now, passengers, as varied and vibrant as the rainbow itself, came from all walks of life. It just so happened that on average, they tipped the scales at around 180 lb. You'd think that's a bit too precise for an estimate, wouldn't you? But you see, in this magical realm, statisticians have fairy dust. And, just like how fairy godmothers knew the exact size of Cinderella's shoe, our statisticians sprinkled their dust and found that passenger weights in our story followed a 'normal distribution'. Quite like the shape of a bell, but let's imagine it as an enchanted hill with the most common weights at the peak and the rare, lighter and heavier weights as the slopes on either side. The enchantment was such that the weights of passengers varied by around 43 lb on either side of 180 lb.

Now, HappiNess was as robust as she was sprightly, but every ship, no matter how bright and yellow, has its limits. She could carry a merry crowd of 25 passengers at a time. Any more than that and she'd risk becoming the 'GrumpiNess', and no one wanted that! Besides, she was rated for a load limit of 3500 lb - that's the magic number beyond which HappiNess would start losing her cheer.

Imagine one fine day, a crowd of 25 average-sized passengers (each 180 lb) decided to board HappiNess. That would be quite an adventure, right? Because 25 passengers, each weighing 180 lb, totals to 4500 lb - a number that exceeds the HappiNess' load limit of 3500 lb. And we'd never want to risk her becoming GrumpiNess, would we?

So, we better make sure that we don't overburden HappiNess, even if that means fewer tales of seafaring adventures. The key is to ensure a balance, quite literally, so she can continue to be the HappiNess we all love and enjoy. After all, it's all about staying afloat and riding the waves with a smile, isn't it?

User Helder Lucas
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