Find these probabilities for a standard normal random variable Z. Be sure to dra

Question

Find these probabilities for a standard normal random variable Z. Be sure to draw a picture to check your calculations. Use the normal table or software.

(a) P(Z < 1.5) = __________ (Round to four decimal places as needed.)

(b) P(Z > -1.1) = __________ (Round to four decimal places as needed.)

(c) P( |Z| < 1.6) = __________ (Round to four decimal places as needed.)

(d) P( |Z| > 0.6) = __________ (Round to four decimal places as needed.)

(e) P( -1.1 Z 1.5) = __________ (Round to four decimal places as needed.)

Explanation / Answer

a) P(Z < 1.5)

Using the standard normal table to find this area.

We conclude that:

P ( Z<1.5 )=0.9332

b) Using the standard normal table to find this area.

P ( Z>1.1 )

=P ( Z<1.1 )=0.8643

c) Using the standard normal table to find this area.

P ( Z<1.6 )=0.9452

d) P ( Z>0.6 )

=1P ( Z<0.6 )

=10.7257

=0.2743

e) P ( Z<1.5 )=0.9332.

P ( Z<1.1 ) can be found by using the following standard normal table.

Standard Normal Table

We see that P ( Z<1.1 )=0.8643 so,

P ( Z<1.1)

=1P ( Z<1.1 )

=10.8643

=0.1357

At the end we have:

P (1.1<Z<1.5 )=0.7975

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