It has been noted that Roger Ebert and Paul McCartney were born on the same day (year, month and day). How many such coincidences should you expect?
To make things specific, assume there are 1000 celebrities of such stature and recency, and that whatever their average age is, the standard deviation of their ages is 12 years and follows a normal distribution. Of course the date is rounded to the day; don't worry about the hours.
Feel free to vary the assumptions for bonus answers.
First, Steve is right about my undercounting pairs.
As for the distribution, I see no reason to expect a normal or a uniform distribution. Rather I'd expect a highly negatively skewed bell curve.
Even among the famous it is rare to become so before the age of 20. Many become so in their 20s and 30s. Obama burst onto the scene at the age of 42, but probably didn't make the top 1000 until his nomination 4 years later. Samuel L. Jackson is very well known but really only became noteworthy in his late 40's. Once you become a celebrity you tend to stay one for a long time. Maybe for the rest of your life. We all love Betty White and she's made it to 99.
I'd guess the peak of the curve would be around 70, full of musicians and actors first notable in the 1960's and 70's. With a long tail on the left (Millie Bobby Brown, Adele) and a shorter on on the right for those still alive (Clint Eastwood is 91)
All in all, this would be a fascinating topic for discussion if I were still teaching statistics.
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Posted by Jer
on 2021-10-02 17:14:57 |
On the age distribution
