Solution:
Given μ=126 and σ=22
a)
we have P( x <= 100) = P( x < = x - μ / μ)= ( 99.5 -126 /22 ) = -1.204
P ( X <= -1.204)
= P( Z < -1.204)
=1−P ( Z<1.204 )
=1−0.8849
=0.1151
b) Given that P( 95 ≤ X ≤ 100)
P( 95 ≤ X ≤ 100) = P( 94.5 - 126 /22 ≤ X ≤ 100 -126/ 22)
= ( -1.431 ≤ X ≤ -1.181 )
P( -1.431 ≤ X ≤ -1.181 ) = P( -1.431 ≤ Z ≤ -1.181 )
= 0.0426 ( by standard normal table)
c) given that P(X ≤ x) =0.410
x =μ - Z* σ = 126 - ( 0.2275 *22) = 120.995
X = 120.995 -0.5 = 121.495
d) given that P(X ≤ x) =0.820
x =μ - Z* σ = 126 + ( .9513*22) = 146.137
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