Question

Answer for all please

Answer 1

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

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