The weights of parcels that are dropped off at a local shipp

The weights of parcels that are dropped off at a local shipping center can be represented by a random variable X that is normally distributed with mean mux = 70 and standard deviation x = 10. Determine the following: P[X>50]. P[x

Solution

Normal Distribution
Mean ( u ) =70
Standard Deviation ( sd )=10
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 50) = (50-70)/10
= -20/10 = -2
= P ( Z >-2) From Standard Normal Table
= 0.9772  
b)
P(X < 60) = (60-70)/10
= -10/10= -1
= P ( Z <-1) From Standard Normal Table
= 0.1587                  
c)          
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 60) = (60-70)/10
= -10/10 = -1
= P ( Z <-1) From Standard Normal Table
= 0.15866
P(X < 90) = (90-70)/10
= 20/10 = 2
= P ( Z <2) From Standard Normal Table
= 0.97725
P(60 < X < 90) = 0.97725-0.15866 = 0.8186