We appreciate your visit to An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect a Use a binomial distribution to find the probability. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
This problem can be solved using a binomial distribution. A binomial distribution applies when you have a fixed number of trials, each trial has two possible outcomes, and the probability of success is constant. We should however be cautious given the very small probability of defect, a Poisson distribution may be a better fit.
Explanation:
The solution to this question involves using a binomial distribution. A binomial distribution applies when you have a fixed number of trials, each trial has two potential outcomes (success/failure), and the probability of success is the same for each trial.
In this context, the trials are the cars produced by the automobile manufacturer, a success is a car with a manufacturing defect, and a failure is a car without a manufacturing defect.
The probability of success (p) is given as 1 in 2500 or 0.0004. The number of successes (n) we're interested in is 4 cars.
The formula for the binomial distribution is:
(n choose x)(p^x)(q^(n-x))
Where n is the total number of trials, x is the number of successes, p is the probability of success on a single trial, and q is the probability of failure on a single trial (1-p).
To find the probability of exactly 4 cars with the defect we'll need to specify a number of trials, let's say for 10,000 cars produced (n), then calculate using the above formula.
One must be cautious though, binomial distribution can be a reasonable approximation when the probability of success is small and the number of trials is large, however for very small probabilities like 0.0004 Poisson distribution may usually be a better approximation.
Learn more about Binomial Distribution here:
https://brainly.com/question/33656163
#SPJ11
Thanks for taking the time to read An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect a Use a binomial distribution to find the probability. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
