Editing Openai/6924d898-a68c-8009-beac-944d19ca0daf (section)

==== Subtract the first equation from the second: ====

100−μσ−1−μσ=0.84−(−3.09)\frac{100-\mu}{\sigma} - \frac{1-\mu}{\sigma} = 0.84 - (-3.09)σ100−μ−σ1−μ=0.84−(−3.09)
Left side:

99σ\frac{99}{\sigma}σ99
Right side:

0.84+3.09=3.930.84 + 3.09 = 3.930.84+3.09=3.93
So:

99σ=3.93⇒σ≈993.93≈25.2\frac{99}{\sigma} = 3.93 \Rightarrow \sigma \approx \frac{99}{3.93} \approx 25.2σ99=3.93⇒σ≈3.9399≈25.2
Now plug back into one equation, say the second:

100−μ25.2=0.84\frac{100-\mu}{25.2} = 0.8425.2100−μ=0.84
100−μ=0.84×25.2≈21.2100 - \mu = 0.84 \times 25.2 \approx 21.2100−μ=0.84×25.2≈21.2
μ≈100−21.2≈78.8\mu \approx 100 - 21.2 \approx 78.8μ≈100−21.2≈78.8
So the mean of the flip—where the normal CDF gives Luffy a 50% chance—is around:

: 

That’s your P=0.5P = 0.5P=0.5 point.