Question

# Z is a standard normal random variable. Compute the following probabilities. a. P(-1.33 Z 1.67) b....

Z is a standard normal random variable. Compute the following probabilities.

 a. P(-1.33 Z 1.67) b. P(1.23 Z 1.55) c. P(Z 2.32) d. P(Z -2.08) e. P(Z -1.08)

Solution :-

a)

P ( - 1.33 < Z < 1.67 ) = P ( Z < 1.67 ) - P ( Z < - 1.33 )

By Using Standard Normal Table,

P ( - 1.33 < Z < 1.67 ) = 0.9525 - 0.0918

P ( - 1.33 < Z < 1.67 ) = 0.8607

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b)

P ( 1.23 < Z < 1.55 ) = P ( Z < 1.55 ) - P ( Z < 1.23 )

By Using Standard Normal Table,

P ( 1.23 < Z < 1.55 ) = 0.9394 - 0.8907

P ( 1.23 < Z < 1.55 ) = 0.0487

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c)

P ( Z > 2.32 ) = 1 - P ( Z < 2.32 )

By Using Standard Normal Table,

P ( Z > 2.32 ) = 1 - 0.9898

P ( Z > 2.32 ) = 0.0102

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d)

By Using Standard Normal Table,

P ( Z < - 2.08 ) = 0.0188

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e)

By Using Standard Normal Table,

P ( Z < - 1.08 ) = 0.1401

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