Given,
= 84 , = 20
We convert this to standard normal as
P(X < x) = P(Z < ( x - ) / )
a)
P(X > 100) = P(Z > ( 100 - 84) / 20)
= P(Z > 0.8)
= 0.2119
b)
P( 80 < X < 144 ) = P(X < 144) - P(X < 80)
= P(Z < ( 144 - 84) / 20) - P(Z < ( 80 - 84) / 20)
= P(Z < 3) - P(Z < -0.2)
= 0.9987 - 0.4207
= 0.5780
c)
P( 124 < X < 160 ) = P(X < 160) - P(X < 124)
= P(Z < ( 160 - 84) / 20) - P(Z < ( 124 - 84) / 20)
= P(Z < 3.8 ) - P(Z < 2)
= 0.9999 - 0.9772
= 0.0227
d)
P(X < 50) = P(Z < (50 - 84) / 20)
= P(Z < -1.7)
= 0.0446
e)
P(X > x*) = 0.0062
So,
P(X < x*) = 0.9938
P(Z < (x* - ) / ) = 0.9938
From Z table, z-score for the probability of 0.9938 is 2.50
So,
(x* - ) / = 2.50
x* - 84 / 20 = 2.50
x* = 134
Suppose the random variable X follows a normal distribution with mean µ = 84 and standard...
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