Amachine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 4 cm and standard deviation 0.2 cm. the specifications call for corks with diameters between 3.8 and 4.2 cm. a cork not meeting the specifications is considered defective. (a cork that is too small leaks and causes the wine to deteriorate; a cork that is too large doesn't fit in the bottle.) what proportion of corks produced by this machine are defective? (round the answer to four decimal places.)

0.3173

Step-by-step explanation:

Given : A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with

and

The specifications call for corks with diameters between 3.8 and 4.2 cm.

Let x be the random variable that represents the  the diameter of the corks.

Using formula , the z-score corresponding to x= 3.8 will be :_

z-score corresponding to x= 4.2 will be :_

Now, by using the standard normal distribution table for z, we have

∴The proportion of corks produced by this machine are meeting the specifications=0.6827

∴The proportion of corks produced by this machine are defective =

step-by-step explanation: