Answered: A machine that cuts corks for wine…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of corks is well approximated by a Normal distribution with mean 3 cm and standard deviation 0.1 cm.

The specififications call for corks with diameters between 2.9 and 3.1 cm. A cork not meeting the specififications is considered defective (a cork that is too small leaks and causes the wine to deteriorate; a cork that is too large does not fifit in the bottle).

(a) What proportion of corks produced by this machine are defective?

(b) If you choose 15 corks at random produced by this machine, what is the probability that 5 of them will be defective?

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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