percentiles and probability The amount of cola put into 1 li

percentiles and probability

The amount of cola put into 1 liter (33.8 ounces) bottles by an automatic filling machine is normally distributed with a mean µ and standard deviation = 0.25 ounces. The value of µ can be adjusted, but is the same regardless of the adjustment.

If the machine is adjusted so that µ = 34.0, what is the probability that a randomly selected bottle has more than 33.8 ounces of soda?

If the machine is adjusted so that µ = 33.6, what is the probability that a randomly selected bottle is under-filled (that is, has less than 33.8 ounces of soda)?

Solution

Normal Distribution
Mean ( u ) =34
Standard Deviation ( sd )=0.25
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 33.8) = (33.8-34)/0.25
= -0.2/0.25 = -0.8
= P ( Z >-0.8) From Standard Normal Table
= 0.7881                  
P(X < 33.8) = (33.8-33.6)/0.25
= 0.2/0.25= 0.8
= P ( Z <0.8) From Standard Normal Table
= 0.7881