Question

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

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.

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

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