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

Let X be the random variable denoting the clotting time of an individual.

Thus, X ~ N(7.45, 3.6) i.e. (X - 7.45)/3.6 ~ N(0,1)

The probability that an individual's clotting time will be less than 4 seconds or greater than 13 seconds = P(X < 4) + P(X > 13) = 1 - P(4 < X < 13) = 1 - P[(4 - 7.45)/3.6 < (X - 7.45)/3.6 < (13 - 7.45)/3.6] = 1 - P[-0.9583 < (X - 7.45)/3.6 < 1.5417] = 1 - [(1.5417) - (-0.9583)] = 1 - [0.9384 - 0.1690] = 1 - 0.7694 = 0.2306

[(.) is the cdf of N(0,1)]