Question

Make a sketch to illustrate what each statement represents. Refer to your calculator or Table 2 (z-score table) to find the following. Use the closest value if necessary. Show the procedure you used to find your answers. (a) P(–2.01 < z < 1.28) (b) the value of z* for which P(z ≥ z*) = 0.27 (c) the value of z* for which P(–z* < z < z*) = 0.80

Answer 1

Solution:

Given that,

a ) P(–2.01 < z < 1.28)

P ( Z < 1.28 ) - P ( Z < -2.01 )

Using standard normal table.

= 0.8997 - 0.0222

= 0.8775

Probability = 0.8775

b) P( Z z*) = 0.27

P( Z   z*) = 1 - 0.27

P( Z   z*) = 0.83

Using standard normal table.

z* = 0.95

c) P(– z* < Z < z* ) = 0.80

P(Z < z* ) - P(Z < – z* ) = 0.80

2P(Z < – z* ) - 1 = 0.80

2P(Z < z* ) = 1 + 0.80

2P(Z < z* ) = 1.80

P(Z < z* ) = 1.80 / 2 = 0.90

P(Z < z* ) = 0.90

z* = 1.28

- z* = - 1.28