We have:
P(x<25000)=0.55
P(x>56000)=0.15
P(25000≤x≤56000)=0.3
Let a is mean, σ is standard deviation. Then
Φ(σ25000−a)−Φ(−∞)=0.55⇒Φ(σ25000−a)+0.5=0.55⇒Φ(σ25000−a)=0.05
Φ(∞)−Φ(σ56000−a)=0.15⇒0.5−Φ(σ56000−a)=0.15⇒Φ(σ56000−a)=0.35
Φ(σ56000−a)−Φ(σ25000−a)=0.3
If Φ(σ25000−a)=0.05 then σ25000−a=0.13.
If Φ(σ56000−a)=0.35 then σ56000−a=1.04 .
We have the system:
{σ25000−a=0.13σ56000−a=1.04⇒{σ=0.1325000−a0.1325000−a56000−a=1.04⇒{σ=0.1325000−a7280−0.13a=26000−1.04a⇒{0.91a=18720σ=0.1325000−a⇒{a=7144000σ=9131000
Answer: a=7144000,σ=9131000
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