If X ~ N (50, 16) then which of the following is not possible.
Answers
Given : X ~ N (50, 16)
To find : which of the following is not possible.
(a) P (X > 60) = 0.30 (b) P (X < 50) = 0.50 (c) P (X < 60) = 0.40 (d) P (X > 50) = 0.50
Solution:
X ~ N (50, 16)
=> Mean = 50
SD = 16
Z score = (Value - Mean)/SD
P (X > 60) = 0.30
for X > 60
=> Z Score = (60 - 50)/16 = 10/16 = 0.625
Z Score 0.625 = 0.734
for X > 60 => 1 -0.734 = 0.266
P (X > 60) = 0.266
Hence P (X > 60) = 0.30 is not possible
P (X < 60) = 0.734
P (X < 60) = 0.40 not possible
P (X < 50) = 0.50
=> Z Score = (50 - 50)/16 = 0 => 0.5
P (X < 50) = 0.50 is possible
P (X > 50) = 0.50 is possible
if we do not use exact z score table
then for X < 60
60 is more than 50
hence P(X < 60) would be more than 0.5
hence can not be = 0.4
hence P(X < 60) = 0.4 not possible
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