Question

# Let 'c' represent the area under the normal curve for which lies between two values,  and ....

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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