Let X= the cannon shell impact position, as measured along the line of fire from the target point: X∼N(μ,σ).
Then Z=σX−μ∼N(0,1)
P(X<−11.2)=P(Z<σ−11.2−μ)=0.1515
σ−11.2−μ≈−1.03002
P(X>95.6)=1−P(X≤95.6)=
=1−P(Z≤σ95.6−μ)=0.0505
P(Z≤σ95.6−μ)=0.9495
σ95.6−μ≈1.64002
95.6−1.64002σ=−11.2+1.03002σ
2.67004σ=106.8
σ=40
μ=95.6−1.64002(40)=30
μ=30 m,σ=40 m
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