/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 For each of the following exerci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 4

For each of the following exercises, determine the range (possible values) of the random variable. A batch of 500 machined parts contains 10 that do not conform to customer requirements. The random variable is the number of parts in a sample of five parts that do not conform to customer requirements.

Short Answer

Expert verified
The range is 0 to 5.

Step by step solution

01

Identify Random Variable

In this exercise, the random variable is defined as the number of non-conforming parts in a sample of five parts taken from the batch of 500 parts.
02

Determine Minimum Value

The smallest number of non-conforming parts that could be in a sample of five is zero. This happens when all five parts in the sample conform to the requirements.
03

Determine Maximum Value

The largest number of non-conforming parts in a sample of five is five. This occurs when all the sampled parts are non-conforming. However, since there are only 10 non-conforming parts in the batch, it is possible for five non-conforming parts to be selected in a single sample.
04

Establish Range of the Random Variable

Considering the minimum value is 0 and the maximum value is 5, the range of the random variable is from 0 to 5.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Discrete Random Variables
A discrete random variable is a type of random variable that can take on a countable number of distinct values. In the context of this exercise, the random variable represents the number of non-conforming parts within a sample of five parts drawn from a batch of 500 parts. Unlike continuous random variables, which can have any value within a range, discrete random variables often take on integer values. These values result from counting processes, such as the number of defective parts in a batch. For this specific problem:
  • The possible values the discrete random variable can take are 0, 1, 2, 3, 4, and 5.
  • These values represent all possible scenarios of picking non-conforming parts from the sample.
Understanding this random variable helps us evaluate the quality and reliability of the production process.
Non-conforming Parts Analysis
Non-conforming parts analysis is critical in quality control as it helps manufacturers determine how many produced items fail to meet specific standards or requirements. This exercise involves analyzing a sample from a larger batch to identify the count of non-conforming parts. By taking a sample:
  • We can estimate the level of conformity or defectiveness in the entire production batch.
  • The goal is to find non-conforming parts before they reach the consumer, ensuring a higher quality product is delivered.
Such an analysis is crucial not only for maintaining product standards but also for minimizing waste and improving efficiency in the manufacturing process. Understanding the distribution of non-conforming parts helps in making more informed decisions about production improvements.
Statistical Sampling
Statistical sampling involves selecting a subset of individuals or items from a larger population to reflect the qualities and characteristics of that population. In this exercise, we analyze a sample of five parts from a total batch of 500. Statistical sampling allows:
  • Businesses to make inferences about a large population without examining every individual part.
  • Organizations to save time and resources while still obtaining reliable information regarding quality or conformity.
There are different techniques to choose samples, including random sampling, systematic sampling, and stratified sampling. In this exercise, by choosing a sample size that is manageable, companies gain insights into the overall production quality and reliability, which are important for maintaining high standards in manufacturing.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Saguaro cacti are large cacti indigenous to the southwestern United States and Mexico. Assume that the number of saguaro cacti in a region follows a Poisson distribution with a mean of 280 per square kilometer. Determine the following: (a) Mean number of cacti per 10,000 square meters. (b) Probability of no cacti in 10,000 square meters. (c) Area of a region such that the probability of at least two cacti in the region is \(0.9 .\)

A congested computer network has a \(1 \%\) chance of losing a data packet, and packet losses are independent events. An e-mail message requires 100 packets. (a) What distribution of data packets must be re-sent? Include the parameter values. (b) What is the probability that at least one packet must be re-sent? (c) What is the probability that two or more packets must be re-sent? (d) What are the mean and standard deviation of the number of packets that must be re-sent? (e) If there are 10 messages and each contains 100 packets, what is the probability that at least one message requires that two or more packets be re- sent?

A manufacturer of a consumer electronics product expects \(2 \%\) of units to fail during the warranty period. A sample of 500 independent units is tracked for warranty performance. (a) What is the probability that none fails during the warranty period? (b) What is the expected number of failures during the warranty period? (c) What is the probability that more than two units fail during the warranty period?

The number of errors in a textbook follows a Poisson distribution with a mean of 0.01 error per page. What is the probability that there are three or fewer errors in 100 pages?

Suppose that \(X\) has a Poisson distribution with a mean of 0.4 . Determine the following probabilities: (a) \(P(X=0)\) (b) \(P(X \leq 2)\) (c) \(P(X=4)\) (d) \(P(X=8)\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.