Normal Distribution (Statistics) 求教, 感激?

設電池壽命之隨機變數為 x , 其標準差為 s

a.
P( x > 115 ) = 0.025
P( Z > (115-100)/s ) = 0.025 , where Z ~ N(0,1)
查標準常態分配表得 P( Z > 1.96 ) = 0.025 , 所以:
(115-100)/s = 1.96
s = 15 / 1.96 ≒ 7.653 (小時) ..... Ans

b.
i
P( x < 94.5 )
= P( Z < (94.5-100)/10 )
= P( Z < - 0.55 )
= 0.2912 ..... Ans

ii
P( x > T ) = 0.9
P( Z > (T-100)/10 ) = 0.9
查表得 P( Z > - 1.28 ) = 0.9 , 所以:
(T-100)/10 = - 1.28
T = 100 + 10*(-1.28) = 87.2 ..... Ans