Find the following probabilities for a normal random variabl

Find the following probabilities for a normal random variable X that has a mean of 15 and a standard deviation of 3.

Solution

a)

z = ( 17-15) / 3 = 0.67

P =0.7486 Answer

b)

z = ( 11-15) / 3 = 0.67

P =1 - 0.0918 = 0.9082 Answer

c)

z1 = ( 10-15) / 3 = -1.67

z2 = ( 14-15) / 3 = -0.33

P = 0.3707 - 0.0475 = 0.3232 Answer

d)

z1 = ( 12-15) / 3 = -1

z2 = ( 20-15) / 3 = 1.67

P = 0.9525- 0.1587= 0.7938 Answer