There are two machines available for cutting corks intended for use in wine bott
ID: 1861970 • Letter: T
Question
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation0.07 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.02 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
What is the probability that the first machine produces an acceptable cork? (Round your answer to four decimal places.)
What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)
Which machine is more likely to produce an acceptable cork?
Explanation / Answer
n the first case, mean = 3 and sd = 0.07, so z scores are:
(3 - 2.9)/0.07 = 1
(3.1 - 3)/0.07= 1
In the second case, mean = 3.05 and sd = 0.08, so z scores are:
(3.04 - 2.9)/0.02 =1.875
3.1 - 3.04)/0.02 = 0.625
In the first case, you have +/- 1 standard deviation which means 68.27% of the corks will meet specifications
In the second case, (0.9392 + 0.4680)/2 = 70.36% of the corks will meet specifications.
These calculations are based on the areas under the standard z-score curve as a function of the calculated z scores above.
The second machine is the better choice.