Question

Find the area under the standard normal curve that lies between the following two z values. Round your answers to at least four decimal places.

(a)Find the area under the standard normal curve that lies between = z − 1.28 and = z 1.36 .

(b)Find the area under the standard normal curve that lies between = z − 2.17 and = z − 1.92 .

(c)Find the area under the standard normal curve that lies between = z 1.36 and = z 1.78 .

(d)Find the area under the standard normal curve that lies between = z − 0.82 and = z 0.98 .

Answer 1

solution

(A) z =− 1.28 and z =1.36

P( − 1.28 < Z < 1.36 )

= P(Z < 1.36 ) - P(Z < − 1.28 )

Using z table,  

= 0.9131-0.1003

area=0.8128  

(B)

P(  − 2.17< Z < − 1.92)

= P(Z <− 1.92 ) - P(Z <  − 2.17)

Using z table,  

= 0.0274-0.015

area=0.0124  

(C)

P( 1.36< Z < 1.78)

= P(Z <1.78 ) - P(Z < 1.36)

Using z table,  

= 0.9625-0.9131

area=0.0494  

(D)

P( − 0.82< Z <  0.98)

= P(Z < 0.98 ) - P(Z < − 0.82)

Using z table,  

= 0.8365-0.2061

area=0.6304