COFFEE MACHINE DISPENSES COFFEE INTO 16 OUNCE CUPS TEST SHOW

COFFEE MACHINE DISPENSES COFFEE INTO 16 OUNCE CUPS. TEST SHOW THAT ACTUAL AMOUNT OF COFFEE DIPENSED IS NORMALLY DISTRIBUTED WITH MEAN OF 15.2 OUCES AND STANDARD DEVIATION OF 0.9 OUNCES. WHAT % OF CUPS WILL RECEIVE LESS THAN 17 OUNCES? AND GREATER THAN 15.2 OUNCES?

Solution

Normal Distribution
Mean ( u ) =15.2
Standard Deviation ( sd )=0.9
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 17) = (17-15.2)/0.9
= 1.8/0.9= 2
= P ( Z <2) From Standard Normal Table
= 0.9772                  
P(X > 15.2) = (15.2-15.2)/0.9
= 0/0.9 = 0
= P ( Z >0) From Standard Normal Table
= 0.5