Exploring the Possibility of People with Negative Height
This article delves into the theoretical concept of people with negative height, discussing the probabilities based on normal distribution models and empirical rules. It explores the likelihood of encountering individuals with negative height in today's population, throughout history, and the number of individuals needed to observe such a case with a high probability. The analysis concludes with insights on the extreme rarity of individuals with negative height.
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Presentation Transcript
When will we see people of negative height? Group 1: Walter (Presenter) Jun Yue Celestine
Outline 1. Normal Distribution to model height. 2. Empirical Rule 3. What is the probability of there being height among people living today? being a fully grown adult with negative body 4. What is the probability of there having negative body height among people who have ever lived on earth? having been been a fully grown adult with 5. How many people are necessary to have ever lived on earth in order to observe at least 1 fully grown human with negative body height with a probability of at least 95%? 6. By when can we expect to reach this necessary number of people ever lived on
Empirical Rule 68.26% of the population lie within 1 SD of the mean 95.44% lie within 2 SDs of the mean 99.73% lie within 3 SDs of the mean 0.27% are more than 3 SDs from the mean. Since we are curious to find out about the extreme case of negative height we look at what proportion lies 18.5 SDs away from the mean? The answer to that is 1.06 x 10^-76. This This is is equivalent equivalent to to say or or negative negative height height say 1 1 person person in in 10 10^ ^76 76 people people will will have have zero zero
What is the probability of there being a fully grown adult with negative body height living among us today? - The world population at the time the article was written : about 7 billion (7 x 10^9) - Fully grown adults: 5.17 billion (5.17 x 10^9) - To get the probability we take the population of fully grown adults divide by 10^76 and it will give us something very small which is often rounded off to zero (5.33x 10^-67) Equivalent to saying 1 chance in 2.33 x 10^66 of seeing a person with negative body height
What is the probability of there having been a fully grown adult with negative body height throughout history? - Number of people who have ever lived on Earth: 107.6 billion - Upper estimate of the probability = 1.11 x 10^-65 - We cannot reject our hypothesis - We cannot be sure that cases of negative height in the early times of mankind would be recorded and come to our knowledge - There may have been a lot of cases of negative height but these people went extinct due to evolution Equivalent to saying 1 chance in 10^-65 of seeing a person with
What is the number of people needed for us to see at least 1 fully grown adult with negative body height with a probability of at least 95%? - Answer: 2.9 10^76 (in words is 29 thousand billion billion billion billion billion billion billion billion people) Equivalent: A computer of the current generation, would need8.75 10^52 years just to count to this number.Also much longer than the age of the earth (estimated to be around 4.6 billion years). The Big Bang is estimated to have occurred about 13.7 billion years ago.
How much time do we need before we can have a large enough sample size to observe this phenomenon? Under certain assumptions we can estimate the time needed to have a large enough sample size. -Using growth rate of the global population, starting global population, life expectancy. -We have to account for life expectancy because every individual contributes in each year of his lifespan to the number of people alive. After factoring everything in and doing the calculations the answer is: 13842 YEARS FROM NOW
Take Home Message All All models models are some some are are useful their their range range at at least Box Box are wrong, wrong, but useful - - for for part least.. - - George but part of of George
