Answered: A machine that cuts corks for wine…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 certain mean and standard deviation. 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.)

Suppose that there are two machines available for cutting corks. The first machine produces corks with diameters that are approximately normally distributed with mean 4.05 cm and standard deviation 0.01 cm. The second machine produces corks with diameters that are approximately normally distributed with mean 4 cm and standard deviation 0.1 cm. Which machine would you recommend? (Hint: Which machine would produce fewer defective corks?)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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