Question

In each case, determine the value of the constant c the makes the probability statement correct.

1. Ф(c) = 0.9838
2. P (0≤ Z ≤ c) =0.291
3. P (c ≤ Z) = 0.121
4. P (-c ≤ Z ≤ c) = 0.668
5. P(c ≤ │Z│) = 0.016

Answer 1

Solution :

Using standard normal table,

a.

= 0.9838

P(Z < z) = 0.9838

P(Z < 2.14) = 0.9838

c = 2.14

b.

P( 0 z c) = 0.291

P(Z c) - P(Z 0) = 0.291

P(Z c) = P(Z 0) + 0.291

P(Z c) = 0.5 + 0.291 = 0.791

P(Z 0.81) = 0.791

c = 0.81

c.

P(c Z) = 0.121

P(Z c) = 0.121

1 - P(Z c) = 0.121

P(Z c) = 1 - 0.121 = 0.879

P(Z 1.17) = 0.879

c = 1.17

d.

P(-c Z c) = 0.668

P(Z c) - P(Z -c) = 0.668

2P(Z c) - 1 = 0.668

2P(Z c) = 1 + 0.668 = 1.668

P(Z c) = 1.668 / 2 = 0.834

P(Z 0.97) = 0.834

c = 0.97

e.

P(c |Z|) = 0.016

2 * [1 - P(z < c)] = 0.016

1 - P(z < c) = 0.016 / 2 = 0.008

P(z < c) = 1 - 0.008 = 0.992

P(z < 2.41) = 0.992

c = 2.41