A machine that cuts corks for wine bottles operates in such

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 mean 4 cm and standard deviation 0.1 cm. The specifications call for corks with diameters between 3.9 and 4.1 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 your answer to four decimal places.)

Solution

a<x<b

a= (2.85-3)/.1 = -1.5

b= (3.15-3)/.1 = 1.5

check the table and the numbers are: -1.5 = .0668 and 1.5 = .9232

then .9232 - .0668 = .8664 (THIS IS NOT THE FINAL ANSWER)

this is where it gets a bit complicated: you need to turn the .8664 into a percent and that becomes 86.64% THAT ARE NOT DEFECTIVE!

so then 100-86.64 = 13.36 % then you just turn this number into a decimal and that is your answer

13.36/100 = .1336 when i submitted my homework it said this answer was correct