Question

Find the following probabilities for the standard normal random variable z. (Round your answers to four decimal places.)

(a) P(?1.41 < z < 0.61) =

(b) P(0.55 < z < 1.78) =

(c) P(?1.54 < z < ?0.44) =

(d) P(z > 1.32) =

(e) P(z < ?4.31) =

You may need to use the appropriate appendix table or technology to answer this question.

Answer 1

Solution:

(a) P(?1.41 < z < 0.61)

P( z < 0.61) - P (z < -1.41 )

Using standard normla table

=0.7291- 0.0793

=0.6498

Probability = 0.6498

(b) P(0.55 < z < 1.78)

P( z < 1.78) - P (z <0.55 )

Using standard normla table

=0.9625- 0.7088

=0.2537

Probability = 0.2537

(c) P(?1.54 < z < ?0.44)

P( z < -0.44) - P (z <-1.54)

Using standard normla table

=0.3300 - 0.0618

=0.2628

Probability = 0.2628

(d) P(z > 1.32)

= 1 -  P(z <1.32)

Using standard normla table

= 1 - 0.9066

=0.0934

Probability = 0.0934

(e) P(z < ?4.31)

Using standard normla table

= 0

Probability = 0