Let X be a random variable which follows a normal distribution with mean 5 and standard deviation 3. (a) P(X 2.5) (c) P(2.5

Question

Let X be a random variable which follows a normal distribution with mean 5 and standard deviation 3. (a) P(X < 7) (b) P(X > 2.5) (c) P(2.5<X <7)

Jon S. · Accepted Answer

use transformation: z = (x - mean)/SD = (x - 5)/3

a) P(x < 7) = P(z < (7-5)/3) = P(z < 0.67). Look up probability in standard normal distribution table

b) P(x > 2.5) = P(z > (2.5-5)/3) = P(z > -0.833) = 1 - P(z < -0.833)

c) P(2.5 < x < 7) = P((2.5-5)/3 < z < (7-5)/3) = P(-0.833 < z < 0.67) = P(z < 0.67) - P(z < -0.833).

or 1 - the sum of the probabilities computed in a) and b).

Let X be a random variable which follows a normal distribution with mean 5 and standard deviation 3. (a) P(X < 7) (b) P(X > 2.5) (c) P(2.5<X <7)