The mean clotting time of blood is 745 seconds with a standa

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 3 seconds or greater than 8 seconds Assume a normal distribution. The probability is

Solution

z = (x - mean)/ stand deviatn

For x = 3, z₁ = (3 - 7.45)/3.6 = -1.24

For x = 8, z₂ = (8 - 7.45)/3.6 = 0.15

P( 3 < x < 8) = P(-1.24 < z < 0.15) = P (z < 0.15) - P ( z< -1.24) = 0.55962 - (1 - P(z<1.24))

= 0.55962 - (1- 0.89251) = 0.55962 - 0.10749 = 0.45213

Probability that an individual\'s clotthing time will be less than 3s and greater than 8s = 1 - P( 3 < x < 8)

= 1 - 0.45213 = 0.54787 = 0.548