Question

The mean clotting time of blood is 7.45 seconds with a standard deviation of 3.6 seconds. What is the probability that an​ individual's clotting time will be less than 4 seconds or greater than 13 ​seconds? Assume a normal distribution. Find the probability.

Answer 1

P(X < 4 or X > 13) = 1 - P(4 < X < 13)

Given :- = 7.45 , = 3.6 )
We convet this to Standard Normal as
P(X < x) = P( Z < ( X - ) / )
P ( 4 < X < 13 ) = P ( Z < ( 13 - 7.45 ) / 3.6 ) - P ( Z < ( 4 - 7.45 ) / 3.6 )
= P ( Z < 1.54) - P ( Z < -0.96 )
= 0.9382 - 0.1685
= 0.7697

P(X < 4 or X > 13) = 1 - 0.7697

= 0.2303