d Find P6 X 14 Round z value to 2 decimal places and final a

d.

Find P(6 X 14). (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.

Solution

Normal Distribution
Mean ( u ) =10
Standard Deviation ( sd )=6
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 6) = (6-10)/6
= -4/6 = -0.6667
= P ( Z <-0.6667) From Standard Normal Table
= 0.25249
P(X < 14) = (14-10)/6
= 4/6 = 0.6667
= P ( Z <0.6667) From Standard Normal Table
= 0.74751
P(6 < X < 14) = 0.74751-0.25249 = 0.4972