Question

The fill amount in 1​-liter soft drink bottles is normally​ distributed, with a mean of 1.0 liter and a standard deviation of 0.05 liter. If bottles contain less than 95​% of the listed net content ​(0.95 ​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 1.08 liters may cause excess spillage upon opening. In an effort to reduce the number of bottles that contain less than 0.95 liter​, the bottler sets the filling machine so that the mean is 1.02 liters. Under these​ circumstances, complete parts​ (a) through​ (e) below.

a. What proportion of bottles contain between 0.95 and ​liters? nothing ​(Round to four decimal places as​ needed.)

b. What proportion of bottles contain between 0.95 and 1.08 ​liters? nothing ​(Round to four decimal places as​ needed.)

c. What proportion of bottles contain below 0.95 liters or above 1.08 ​liters? nothing ​(Round to four decimal places as​ needed.)

d. At least how much soft drink is contained in 96​% of the​ bottles? nothing ​liter(s) ​(Round to two decimal places as​ needed.)

e. Ninety dash six percent of the bottles contain an amount that is between which two values​ (symmetrically distributed) around the​ mean? Between nothing ​liter(s) and nothing ​liter(s) ​(Round to two decimal places as needed. Use ascending​ order.)

Answer 1