assume data is normally distributed round answers to three d

(assume data is normally distributed, round answers to three decimal places)

Solution

Normal Distribution
Mean ( u ) =13
Standard Deviation ( sd )=15
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 13) = (13-13)/15
= 0/15 = 0
= P ( Z >0) From Standard Normal Table
= 0.5                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 9) = (9-13)/15
= -4/15 = -0.2667
= P ( Z <-0.2667) From Standard Normal Table
= 0.39486
P(X < 12) = (12-13)/15
= -1/15 = -0.0667
= P ( Z <-0.0667) From Standard Normal Table
= 0.47342
P(9 < X < 12) = 0.47342-0.39486 = 0.0786                  
c)
P ( Z < x ) = 0.975
Value of z to the cumulative probability of 0.975 from normal table is 1.96
P( x-u/s.d < x - 13/15 ) = 0.975
That is, ( x - 13/15 ) = 1.96
--> x = 1.96 * 15 + 13 = 42.4