Question

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.) The area to the right of z = −1.13 is .

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.) The area to the right of z = −2.15 is .

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.) The area between z = 0 and z = −1.93 is

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.) The area between z = −2.15 and z = 1.34 is

Answer 1

Using standard normal z-table we find the following probabilities,

i) P(Z > -1.13) = P(Z < 1.13) = 0.8708

Therefore, the area to the right of z = -1.13 is 0.8708

ii) P(Z > -2.15) = P(Z < 2.15) = 0.9842

Therefore, the area to the right of z = -2.15 is 0.9842

iii) P(-1.93 < Z < 0)

= P(Z < 0) - P(Z < -1.93)

= P(Z < 0) - [ 1 - P(Z < 1.93) ]

= 0.5000 - [ 1 - 0.9732 ]

= 0.5000 - 0.0268

= 0.4732

Therefore, the area between z = 0 and z = -1.93 is 0.4732

iv) P(-2.15 < Z < 1.34)

= P(Z < 1.34) - P(Z < -2.15)

= P(Z < 1.34) - [ 1 - P(Z < 2.15) ]

= 0.9099 - [ 1 - 0.9842 ]

= 0.9099 - 0.0158

= 0.8941

Therefore, the area between z = -2.15 and z = 1.34 is 0.8941