Question

The fill amount in 11​-liter soft drink bottles is normally​ distributed, with a mean of 1.01.0 literliter and a standard deviation of 0.040.04 liter. If bottles contain less than 9494​% of the listed net content ​(0.940.94 ​liters, in this​ case), the manufacturer may be subject to penalty by the state office of consumer affairs. Bottles that have a net content above 1.051.05 liters may cause excess spillage upon opening. In an effort to reduce the number of bottles that contain less than 0.940.94 literliter​, the bottler sets the filling machine so that the mean is 1.031.03 liters. Under these​ circumstances, complete parts​ (a) through​ (e) below. a. What proportion of bottles contain between 0.940.94 and 1.031.03 ​liters? nothing ​(Round to four decimal places as​ needed.) b. What proportion of bottles contain between 0.940.94 and 1.051.05 ​liters? nothing ​(Round to four decimal places as​ needed.) c. What proportion of bottles contain below 0.940.94 liters or above 1.051.05 ​liters? nothing ​(Round to four decimal places as​ needed.) d. At least how much soft drink is contained in 9696​% of the​ bottles?

Answer 1

Solution:

a)

b)

c)

d)

P ( Z < x ) = 0.96
Value of z to the cumulative probability of 0.96 from normal table is 1.7506

( x-u/s.d < x - 1/0.04 ) = 0.99
That is, ( x - 1/0.04 ) = 1.7506
--> x = 1.7506 * 0.04+ 1 = 1.07