Why You Should Never Trust Elevator Capacity Labels

Introduction

A few weeks ago, a colleague of mine shared a story that left me both amused

and alarmed. During a corporate dinner, he and 19 others decided to pile into

an elevator. The sign said it could hold 20 people, so they figured, why not?

But instead of whisking them up to the next floor, the elevator got stuck. They

were trapped for three long hours until the recovery service finally arrived to

free them.

This incident got me thinking: are the claims about how many people an

elevator can hold really accurate? And as someone with a penchant for numbers,

I decided to dig a little deeper to see what the math had to say about it.

The Elevator Math: Can 20 People Really Fit?

Let’s break down the situation using some basic statistics. The elevator in

question had a maximum load of 1360 kg and a capacity of 20 people. Now, if

we assume the average weight of a person is 70 kg with a standard deviation of

16 kg, we can start to analyze the situation more closely.

Step 1: Average Weight Limit Per Person

To calculate the average weight limit per person, we divide the total maximum

load by the elevator’s capacity:

Step 2: Calculate the Z-Score

The Z-score tells us how far the average weight of the group deviates from the

assumed average. The formula to calculate the Z-score is:

Where:

Step 3: Find the Probability

Using the Z-score of -0.56, we can look up the cumulative probability. This

gives us the probability that the average weight is less than 68 kg. However,

what we’re really interested in is the probability of exceeding this weight, which

is the complement:

This probability turns out to be approximately 0.71 or 71%.

Final Verdict: It’s Risky Business

So, there’s a 71% chance that the combined weight of 20 people will exceed

the elevator’s maximum load of 1360 kg. That’s a significant risk, and it’s no

wonder the elevator got stuck!

The Takeaway

Elevators are a vital part of modern life, but it’s crucial to be aware that the

stated capacities are often theoretical. In practice, factors like the variation

in individual weights can drastically alter the scenario. This little exercise in

probability highlights why you should always be cautious about maxing out an

elevator’s stated capacity.

The next time you see a sign claiming that an elevator can hold 20 people,

it might be wise to think twice. After all, you don’t want to be the one stuck

between floors, waiting for hours to be rescued.

Tip

If you’re ever in doubt, take the stairs. Your heart—and the elevator—will

thank you!