Question

Let the random variable X follow a normal distribution with µ = 19 and σ2 = 8. Find the probability that X is greater than 11 and less than 15.

Answer 1

Solution :

Given that ,

mean = = 19

variance = = 8

standard deviation = = 2.8284

P(x > 11) = 1 - P(x < 11)

= 1 - P((x - ) / < (11 -19) / 2.8284)

= 1 - P(z < -2.83)

= 1 - 0.0023   

= 0.9977

Probability = 0.9977

P(x < 15) = P((x - ) / < (15 19) / 2.8284)

= P(z < -1.41)

= 0.0793

Probability = 0.0793