In a human factor experimental project it has been determine

In a human factor experimental project, it has been determined that the reaction time of a

pilot to a visual stimulus is normally distributed with a mean of 1/2 seconds and a standard

deviation of 2/5 seconds.

a) What is the probability that the reaction time of the pilot takes more than 0.3

seconds?

b) What is the 95th percentile of the reaction time?

Solution

Normal Distribution
Mean ( u ) =0.5
Standard Deviation ( sd )=0.4
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 0.3) = (0.3-0.5)/0.4
= -0.2/0.4 = -0.5
= P ( Z >-0.5) From Standard Normal Table
= 0.6915                  
b)
P ( Z < x ) = 0.95
Value of z to the cumulative probability of 0.95 from normal table is 1.645
P( x-u/s.d < x - 0.5/0.4 ) = 0.95
That is, ( x - 0.5/0.4 ) = 1.64
--> x = 1.64 * 0.4 + 0.5 = 1.158