Answer for all please

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

answer:

c) the x-coordinate of the center of the circle increases by 3