Question

求清晰解题思路，谢谢

Answer 1

unit in 1000km
a)
i)
A~N(45,8^2) or (A-45)/8 ~ N(0,1)
P{A>=40}=P{A-45>=-5}=P{(A-45)/8>=-5/8}=P{(A-45)/8<5/8} = 0.7340 ( lookup the value in N(0,1) )
ii)
A1,A2,A3,A4,A5, P{Ak>=40}=0.7340
P{moreThanHalf}=P{exact3}+P{exact4}+P{exact5}
=C(5,3)P{A1,A2,A3>=40&&A4A5<40}

+C(5,4)P{A1,A2,A3,A4>=40&&A5<40}
+C(5,5)P{all>=40}
=10*.7340^3*(1-.7340)^2 + 5*.7340^4*(1-.7340)+1*.7340^5
=0.8789
b)
P{(B-u)/s>(61-u)/s} = .11 => P{(B-u)/s<=(61-u)/s} = 1-.11=.89 => (61-u)/s = 1.2265
P{(B-u)/s<(42.5-u)/s} = .2 => P{(B-u)/s>(42.5-u)/s} = 1-.2 =.8 => (u-42.5)/s = 0.8416
=> u -> 50.0285, s -> 8.9454