Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 5.0; σ = 2.3 P(3 ≤ x ≤ 6) = ________.

Answer 1

Given,

= 5 , = 2.3

We convert this to standard normal as

P( X < x) = P( Z < x - / )

So,

P(3 <= X <= 6) = P( X <= 6) - P( X <= 3)

= P( X <= 6 - 5 / 2.3) - P( X <= 3 - 5 / 2.3)

= P (Z <=0.4348) - P (Z < -0.8696)

= P (Z <= 0.4348) - ( 1 - P( Z < 0.8696) )

= 0.6682 - ( 1 - 0.8077 ) (Probability calculated from Z table)

= 0.4759