Question

Find ?? from the following probabilities: if μ=160, σ=16

1. a) P(X>x0) =0.8770

2. b) P(X<x0) =0.12

3. c) P(X<x0) =0.97

4. d) P(136≤X≤x0) =0.4808

5. e) P(x0≤X≤204) =0.8185

6. f) P(180≤X≤x0) =0.0919

Answer 1

P(X < x₀) = P(Z < (A - )/)

= 160

= 16

a) P(X > x₀) = 0.8770

P(X < x₀) = 1 - 0.8770 = 0.1230

P(Z < (x₀ - 160)/16) = 0.1230

(x₀ - 160)/16 = -1.16

x₀ = 141.44

b) P(X < x₀) = 0.12

P(Z < (x₀ - 160)/16) = 0.12

(x₀ - 160)/16 = -1.175

x₀ = 141.2

c) P(X < x₀) = 0.97

P(Z < (x₀ - 160)/16) = 0.97

(x₀ - 160)/16 = 1.88

x₀ =190.08

d) P(136≤X≤x0) =0.4808

P(X < x₀) - P(X < 136) = 0.4808

P(X < x₀) - P(Z < (136 - 160)/16) = 0.4808

P(X < x₀) - P(Z < -1.5) = 0.4808

P(X < x₀) - 0.0668 = 0.4808

P(X < x₀) = 0.5476

P(Z < (x₀ - 160)/16) = 0.5476

(x₀ - 160)/16 = 0.12

x₀ = 161.92

e) P(x0≤X≤204) =0.8185

P(X < 204) - P(X < x₀) = 0.8185

P(Z < (204 - 160)/16) - P(X < x₀) = 0.8185

P(Z < 2.75) - P(X < x₀) = 0.8185

0.9970 - P(X < x₀) = 0.8185

P(X < x₀) = 0.1785

P(Z < (x₀ - 160)/16) = 0.1785

(x₀ - 160)/16 = -0.92

x₀ = 145.28

f) P(180≤X≤x0) =0.0919

P(X < x₀) - P(X < 180) = 0.0919

P(X < x₀) - P(Z < (180 - 160)/16) = 0.0919

P(X < x₀) - P(Z < 1.25) = 0.0919

P(X < x₀) - 0.8944 = 0.0919

P(X < x₀) = 0.9863

P(Z < (x₀ - 160)/16) = 0.9863

(x₀ - 160)/16 = 2.21

x₀ = 195.36