Question 1149839: A soft drink company fills two-liter bottles on several different lines of production equipment. The fill volumes are normally distributed with a mean of 1.97 liters and a variance of 0.04 (liter)2.
a. Find the probability that a randomly selected two-liter bottle would contain between 1.95 liters or less.
(2 Marks)
b. Find the probability that a randomly selected two-liter bottle would contain between 2.03 liters or less.
(2 Marks)
c. Find the probability that a randomly selected two-liter bottle would contain between 1.95 and 2.03 liters.
(2 Marks)
d. If X is the fill volume of a randomly selected two-liter bottle, find the value of x for which P(X > x) = 0.3228.
(2 Marks)
e. What is the minimum volume of drink required, in liters, to meet the probability of 2.13 percent.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! variance is sd^2 so sd is 0.2 liters
z=(x-mean)/sd
a. -0.02/0.2=-0.1 probability is 0.4602
b. +0.06/0.2=+0.3 prob is 0.6079
between the two is 0.1577
d. From the table, that is a z=+0.46
so 0.46=x-mean/0.2
0.092=x-mean
x=2.062 or 2.06 liters
e. from inv(norm) that is z=-2.028
-2.028=(x-mean)/sd
=-0.4056=x-mean
x=1.56 liters
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