Question

1. Suppose X~N(0,1), what is Pr (0<X<1.20)

2. Suppose X~N(0,1), what is Pr (0<X<1.96)

3. Suppose X~N(0,1), what is Pr (X<1.96)

4. Suppose X~N(0,1), what is Pr (X> 1.20)

Please use step by step work. I'm struggling with grasping the process. Thank you.

Answer 1

Given,X~N(0,1)

X follows the standard normal distribution.

Where,  μ = 0 and σ = 1

and

we know that , z = X - μ / σ

1.

Pr (0<X<1.20)

= Pr (X<1.20) - Pr (X<0)

= Pr (X - μ / σ < 1.20 - 0 / 1 ) - Pr (X - μ / σ < 0 - 0 / 1 )

= Pr (Z < 1.20 - 0 / 1 ) - Pr(Z < 0 - 0 / 1 )

= Pr(Z<1.20) - Pr(Z<0)

= 0.8849 - 0.500 [ From Z-table]

= 0.3849

2.

Pr (0<X<1.96)

= Pr(Z<1.96) - Pr(Z<0)

= 0.9750 - 0.5000

= 0.4750

3.

Pr (X<1.96) = Pr( Z < 1.96 ) = 0.9750

4.

Pr (X> 1.20)

= 1 - Pr(X<1.20)

= 1 - Pr(Z<1.20)

= 1 - 0.8849

= 0.1151

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