Question

Let X be a random continuous variable distributed as normal (5,4).
Find the probabilities of the following events:
a. P(X<4)
b. P(X>6)
c. P(4<X<6)

Show all steps please, type do not attach a photo.

Answer 1

Answer:

u= 5,0 = 4

a. P(X<4)

x – μ 4 - 5

z = -0.25

P(X<4) = P(z < -0.25)

P(z < -0.25) = 0.4013

P(X<4) = 0.4013

b. P(X>6)

τ – μ 6 - 5

z = 0.25

P(X>6) = 1 - P(z < 0.25)

P(z < 0.25) = 0.5987

P(X>6) = 1 - 0.5987

P(X>6) = 0.4013

c. P(4<X<6)

P(4<X<6) = P(x < 6) - P(x<4)

P(4<X<6) = 0.5987 - 0.4013

P(4<X<6) = 0.1974