Mathematics Asked by Frightlin on December 21, 2021
Let’s say that 10 sumo wrestlers were to squeeze into an elevator that could only hold a max capacity of 2300 pounds. Let’s say that the weight of the sumo wrestlers is normally distributed with a mean of 220 lbs and a standard deviation of 25 pounds, what’s the probability that the elevator is past it’s max cap.?
So far I have that
μ = 220
σ = 25
I thought of (2300-2200)/25
= 4 (but that doesn’t seem right. )
and something like P {X > 2300} = Pr {Z>what apparently 4 would be} = 1 – (something here)
I’m not sure if I’m even doing this problem right.
Let $X_i=text{N}(220,25^2)$ be the weight of the $i^text{th}$ wrestler.
Then $X=sum_iX_i$ be the total weight.
Now read http://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables and http://en.wikipedia.org/wiki/Fubini's_theorem and note that Fubini's theorem applies to random variables.
Answered by Dale M on December 21, 2021
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