The fill amount in 2-liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. if bottles contain less than 95% of the listed net contents (1.90 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 2.10 liters may cause excess spillage upon opening. what proportion of the bottles will contain: (a). between 1.90 and 2.0 liters? (b). between 1.90 and 2.10 liters? (c). below 1.90 or above above 2.10 liters?

A. 47.725% of the bottles will have between 1.90 and 2.0 liters  b. 95.450% of the bottles will have between 1.90 and 2.10 liters  c. 4.55% of the bottles will have less than 1.90 or more than 2.10 liters.    For those bottles that have from 1.90 to 2.00 liters, you need to figure out how many standard deviations below the mean they are. Since the mean is 2.0, just subtract 1.90 from it giving 0.10 liters. Now divide that by the standard deviation of 0.05 giving a deviation of 2Ď. Using a lookup table, you'll see that you will be within a 2Ď deviation from the normal, 95.4499736% of the time. Since you're only interested in the lower half of that range, just divide by 2 to get 47.725% of the bottles will have between 1.90 and 2.0 liters. For the full 1.90 and 2.10 range, use the 2Ď value of 95.45%. Finally, for those bottles outside the range, just subtract the 95.45% from 100% giving you 4.55%