Question

Determine the standard normal (z) curve areas below. (Round all answers to four decimal places.)

(a) The area under the z curve to the left of 1.74


(b) The area under the z curve to the left of -0.67


(c) The area under the z curve to the right of 1.3


(d) The area under the z curve to the right of -2.82


(e) The area under the z curve between -2.22 and 0.53


(f) The area under the z curve between -2 and 2


(g) The area under the z curve between -4 and 4

Answer 1

Solution:

Using standard normal table,

a ) P (z < 1.74 )

P (z < 1.74 ) = 0.9591

The area = 0.9591

b ) P (z < - 0.67 )

= 0.2514

P (z <- 0.67 ) = 0.2514

The area = 0.2514

c ) P (z > 1.3 )

= 1 - P (z < 1.3)

= 1 - 0.9032

= 0.0968

P (z > 1.3 ) = 0 0968

The area = 0.0968

d ) P (z > - 2.82 )

= 1 - P (z < - 2.82 )

= 1 - 0.0024

= 0.9976

P (z > 1.3 ) = 0 9976

The area = 0.9976

e ) P ( -2.22 < z < 0.53 )

= P ( z < 0.53 ) - P ( z < - 2. 22 )

= 0.7019 - 0.0132

= 0.6887

P ( -2.22 < z < 0.53 ) = 0.6887

The area = 0.6887

f ) P ( - 2.< z < 2)

= P ( z < 2 ) - P ( z < - 2 )

= 0.9772 - 0.0228

= 0.9544

P ( -2. < z < 2 ) = 0.9544

The area = 0.9544

g ) P ( - 4 < z < 4 )

= P ( z < 4 ) = P ( z < - 4 )

= 1 - 0

= 1.0000

P ( - 4 < z < 4 ) = 1.0000

The area = 1.0000