Answer:
a)
mean of the Standard normal distribution is μ = 0
Standard deviation of the Standard normal distribution σ = 1
b) P( Z < 1.96) = 0.9744
c)
P( - 0.41 < Z) = 0.6591
d) h = 0.3
Step-by-step explanation:
Step(i):-
a)
Given X be a continuous random variable in Normal distribution
The Normal distribution for μ = 0 and σ = 1 is known as Standard normal distribution
mean of the Standard normal distribution is μ = 0
Standard deviation of the Standard normal distribution σ = 1
b)
P( Z < 1.96) = 0.5 + A(1.96)
= 0.5 + 0.4744
= 0.9744
P( Z < 1.96) = 0.9744
c)
P( - 0.41 < Z) = P(Z > -0.41)
= 0.5 +A(-0.41) (∵ A(-0.41) = A(0.41)
= 0.5 + 0.1591
= 0.6591
P( - 0.41 < Z) = 0.6591
d)i) If h >0
P( z < h) = 0.20
⇒ 0.5 +A(z) = 0.20
⇒ A(Z) = 0.20 - 0.5
⇒ A(Z) = - 0.3
h = -0.3
if h < 0
P( z < h) = 0.20
⇒ 0.5 -A(z) = 0.20
⇒ A(Z) =0.5 - 0.2
⇒ A(Z) = 0.3
h = 0.3
