Question

Given N~(5,1) Find the probability that P[X > 5 ] , P[3.5 < X < 5.5], and that P[X<2]

Answer 1

Solution :

Given that ,

mean = = 5

standard deviation = = 1

P(x > 5) = 1 - P(x < 5)

= 1 - P((x - ) / < (5 - 5) / 1)

= 1 - P(z < 0)

= 1 - 0.5

= 0.5

Probability = 0.5

P(3.5 < x < 5.5) = P((3.5 - 5)/ 1) < (x - ) / < (5.5 - 5) / 1) )

= P(-1.5 < z < 0.5)

= P(z < 0.5) - P(z < -1.5)

= 0.6915 - 0.0668

= 0.6247

Probability = 0.6247

P(x < 2) = P((x - ) / < (2 - 5) / 1)

= P(z < -3)

= 0.0013

Probability = 0.0013