Question

X has a normal distribution with the given mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 40, σ = 20, find P(32 ≤ X ≤ 42)

Answer 1

Given :- = 40 , = 20 )
We convet this to Standard Normal as
P(X < x) = P( Z < ( X - ) / )
P ( 32 < X < 42 ) = P ( Z < ( 42 - 40 ) / 20 ) - P ( Z < ( 32 - 40 ) / 20 )
= P ( Z < 0.1) - P ( Z < -0.4 )
= 0.5398 - 0.3446 (From Z table )
= 0.1952