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Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 4 - Problem 38e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 4 - Problem 38e

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# There are two machines available for cutting corks ISBN: 9780321629111 32

## Solution for problem 38E Chapter 4

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 38E

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 deviation .1 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation .02 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. Which machine is more likely to produce an acceptable cork?

Step-by-Step Solution:

Answer : Step 1 : Given,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 deviation .1 cm. Machine 1 : Given mean = 3and standard deviation = 0.1. Acceptable corks have diameters between 2.9 cm and 3.1 cm. = P(2.9 x 3.1) x x = ( z ) Substitute x,and . = ( 2.93 z 3.13) 0.1 0.1 = ( 0.1 z 0.1) 0.1 0.1 = ( 1 z 1) P = 0.6826 Therefore first machine is 0.6826. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation .02 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. Machine 2 : Given mean = 3.04 and standard deviation = 0.2 Acceptable corks have diameters between 2.9 cm and 3.1 cm. = P(2.9 x 3.1) x x = ( z ) Substitute x,and . = ( 2.93.04 z 3.13.04) 0.02 0.02 = ( 0.14 z 0.06) 0.02 0.02 = ( 7 z 3) P = 0.9987 So machine1: P = 0.6826 and machine1: P = 0.9987. We see that probability for machine 2 > machine 1 So,machine 2 is more likely to produce an cork.

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##### ISBN: 9780321629111

The answer to “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 deviation .1 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation .02 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. Which machine is more likely to produce an acceptable cork?” is broken down into a number of easy to follow steps, and 74 words. Since the solution to 38E from 4 chapter was answered, more than 581 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 38E from chapter: 4 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. This full solution covers the following key subjects: corks, diameters, produces, mean, standard. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111.

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