Let 'c' represent the area under the normal curve for which lies between two values, and . Find the value of that is associated to the following values of 'c'.
a) c = 0.95,
b) c = 0.97,
c) c = 0.99,
d) c = 0.995,
Solution,
Using standard normal table,
a) P( -c < Z < c) = 0.95
= P(Z < c) - P(Z <-c ) = 0.95
= 2P(Z < c) - 1 = 0.95
= 2P(Z < c) = 1 + 0.95
= P(Z < c) = 1.95 / 2
= P(Z < c) = 0.975
= P(Z < 1.96) = 0.975
= c = -1.96 and 1.96
b) P( -c < Z < c) = 0.97
= P(Z < c) - P(Z <-c ) = 0.97
= 2P(Z < c) - 1 = 0.97
= 2P(Z < c) = 1 + 0.97
= P(Z < c) = 1.97 / 2
= P(Z < c) = 0.985
= P(Z < 2.17) = 0.985
= c = -2.17 and 2.17
c) P( -c < Z < c) = 0.99
= P(Z < c) - P(Z <-c ) = 0.99
= 2P(Z < c) - 1 = 0.99
= 2P(Z < c) = 1 + 0.99
= P(Z < c) = 1.99 / 2
= P(Z < c) = 0.995
= P(Z < 2.58) = 0.995
= c = -2.58 and 2.58
d) P( -c < Z < c) = 0.995
= P(Z < c) - P(Z <-c ) = 0.995
= 2P(Z < c) - 1 = 0.995
= 2P(Z < c) = 1 + 0.995
= P(Z < c) = 1.995 / 2
= P(Z < c) = 0.9975
= P(Z < 2.81) = 0.9975
= c = -2.81 and 2.81
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