Many electronic 3cigarettes work by vaporizing a liquid mixt

Many electronic (3-)cigarettes work by vaporizing a liquid mixture of flavors, propylene glycol, and (usually) nicotine that is contained in a cartridge. When the smoker inhales on the e-cigaratte, the liquid passes through a heating element and turns to a mist. Of important to a manufacturer and consumer is the number of \"puffs\" that a cigarette can deliver before the cartridge needs to be replaced. A puff is defined as One manufacturer notes that the number of puffs that its cartridge can deliver is actually a normally distributed random variable with a mean of 242 puffs and a standard deviation of 16 puffs. The manufacturer will replace a customer\'s cartridge free of change if it gives to few puffs. Suppose the manufacturer wants to replace no more than 1% of its cartridges. How many puffs should the manufacturer guarantee that a cartridge can produce? Round down to the nearest whole puff.

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.01      
          
Then, using table or technology,          
          
z =    -2.326347874      
          
As x = u + z * s,          
          
where          
          
u = mean =    242      
z = the critical z score =    -2.326347874      
s = standard deviation =    16      
          
Then          
          
x = critical value =    204.778434= 204 [ANSWER]