Question

a)Find the area under the standard normal curve between z = -1.86 and z = 1.1, P(-1.86 < z < 1.1). (Give your answer correct to four decimal places.)

b)Find the area under the standard normal curve between z = -2.53 and z = 1.4, P(-2.53 < z < 1.4). (Give your answer correct to four decimal places.)

c)Consider the normal curve. (Give your answers correct to four decimal places.)

1) Find the area to the right of z = 0.00.


2) Find the area to the right of z = 1.19

3) Find the area to the right of z = -1.4.


4) Find the area to the left of z = 1.75.


5) Find the area to the left of z = -1.75.

d)Consider the following. (Give your answers correct to four decimal places.)

(a) Find P(0.00 < z < 2.15).


(b) Find P(-1.87 < z < 2.07).


(c) Find P(z > 0.10).


(d) Find P(z < 1.53).

Answer 1

a) P(-1.86 < Z < 1.1)

= P(Z < 1.1) - P(Z < -1.86)

= 0.8643 - 0.0314

= 0.8329

b) P(-2.53 < Z < 1.4)

= P(Z < 1.4) - P(Z < -2.53)

= 0.9192 - 0.0057

= 0.9135

c) 1) P(Z > 0)

= 1 - P(Z < 0)

= 1 - 0.5000

= 0.5000

2) P(Z > 1.19)

= 1 - P(Z < 1.19)

= 1 - 0.8830

= 0.1170

3) P(Z > -1.4)

= 1 - P(Z < -1.4)

= 1 - 0.0808

= 0.9192

4) P(Z < 1.75)

= 0.9599

5) P(Z < -1.75)

= 0.0401

a) P(0 < Z < 2.15)

= P(Z < 2.15) - P(Z < 0)

= 0.9842 - 0.5

= 0.4842

b) P(-1.87 < Z < 2.07)

= P(Z < 2.07) - P(Z < -1.87)

= 0.9808 - 0.0307

= 0.9501

c) P(Z > 0.1)

= 1 - P(Z < 0.1)

= 1 - 0.5398

= 0.4602

d) P(Z < 1.53)

= 0.9370