Question

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,

Answer #1

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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