Question

Let X be a normal random variable with parameters ? = 3 and ?² = 2² . Use the standard normal distribution table. Compute the following:

(a) P (X > 2).

(b) P (1.2 < X < 4.5).

Answer 1

Solution :

Given that ,

mean = = 3

standard deviation = = 4.6904

(a)

P(x > 2) = 1 - P(x < 2)

= 1 - P[(x - ) / < (2 - 3) / 4.6904)

= 1 - P(z < -0.21)

= 1 - 0.4168

= 0.5832

P(x > 2) = 0.5832

(b)

P(1.2 < x < 4.5) = P[(1.2 - 3)/ 4.6904) < (x - ) /  < (4.5 - 3) / 4.6904) ]

= P(-0.38 < z < 0.32)

= P(z < 0.32) - P(z < -0.38)

= 0.6255 - 0.352

= 0.2735

P(1.2 < x < 4.5) = 0.2735