Question

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

(a) P(−1.43 < z < 0.64) =

(b) P(0.52 < z < 1.75) =

(c) P(−1.56 < z < −0.48) =

(d) P(z > 1.39) =

(e) P(z < −4.34) =

Answer 1

Solution:

a) To find P ( -1.43 < z < 0.64)

= P( z < 0.64 ) - P( z < -1.43)

= 0.7389 - 0.0764. From Z table

= 0.6625

P( -1.43 < z < 0.64 ) = 0.6625

b) To find P( 0.52 < z < 1.75)

= P( z < 1.75 ) - P( z < 0.52)

= 0.9599 - 0.6985. From Z table

= 0.2614

P( 0.52 < z < 1.75) = 0.2614

c) To find P( -1.56 < z < -0.48)

= P( z < -0.48) - P( z < -1.56)

= 0.3156 - 0.0594. From Z table

= 0.2562

P( -1.56 < z < -0.48) = 0.2562

d) To find P( z > 1.39)

= P( z > 1.39)

= 0.0823 From Z table

e) To find P( z < -4.34)

= P( z < - 4.34)

=0.0000. From Excel

P( z < -4.34) = 0.0000