Determine the probabilities for the following standard normal random variable A-

Question

Determine the probabilities for the following standard normal random variable A-Z P(-1 < Z < 1) B- P(-2 < Z < 2) C- P(-3 < Z < 3) D- P( Z > 31) E- P(0 < Z < 1) Determine the probabilities for the following standard normal random variable A-Z P(-1 < Z < 1) B- P(-2 < Z < 2) C- P(-3 < Z < 3) D- P( Z > 31) E- P(0 < Z < 1) Determine the probabilities for the following standard normal random variable A-Z P(-1 < Z < 1) B- P(-2 < Z < 2) C- P(-3 < Z < 3) D- P( Z > 31) E- P(0 < Z < 1)

Explanation / Answer

a) Here the required probability is computed as:

P( -1 < Z< 1)

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

Getting the above probabilities from the standard normal tables, we get:

= 0.8413 - 0.1587

= 0.6826

b) Here the required probability is computed as:

P( -2 < Z< 2)

= P( Z < 2) - P(Z < -2)

Getting the above probabilities from the standard normal tables, we get:

=0.9772 - 0.0228

= 0.9544

c) Here the required probability is computed as:

P( -3 < Z< 3)

= P( Z < 3) - P(Z < -3)

Getting the above probabilities from the standard normal tables, we get:

=0.9987- 0.0013

= 0.9974

d) P(Z > 31 )

31 is a very large value and therefore P(Z > 31 ) = 0

e) P(0 < Z< 1 )

= P(Z < 1) - P(Z < 0)

= 0.8413 - 0.5

= 0.3413

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