If X follows Normal distribution then
(x - ) / follows standard normal distribution
A.
P(X < 19)
= P{(x -) < (19 - 7)/7}
= P( Z < 1.71)
= 1 - P( Z > 1.71)
= 1 - 0.0436
= 0.9564
0.9564 proportion of population is less than 19
B.
P( X > 4)
= P{(x -) > (4 - 7)/7}
= P( Z > - 0.43)
= 1 - P(Z < - 0.43)
= 1 - P( Z > 0.43)
(since standard normal distribution is symmetric around zero)
= 1 - 0.3336
= 0.6664
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