**Quality Control: Syringes**The quality control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of eight syringes taken from a batch. Suppose the batch contains 1% defective syringes.(a) Make a bar graph showing the probabilities of \( r = 0, 1, 2, 3, 4, 5, 6, 7, \) and 8 defective syringes in a random sample of eight syringes.(b) Find \( \mu \). What is the expected number (\( \mu \)) of effective syringes the inspector will find?(c) What is the probability that the batch will be accepted?(d) Find \( \sigma \). **Explanation:**- **Bar Graph:** You are tasked with creating a bar graph that represents the probability distribution of finding 0 to 8 defective syringes in a sample size of eight. Each bar should represent the probability of exactly \( r \) defective syringes.- **Expected Number (\( \mu \)):** This refers to the mean number of effective syringes the inspector is expected to find in their sample.- **Probability of Acceptance:** This is based on the condition that a batch is accepted if fewer than two defective syringes are found. Calculate the probability that 0 or 1 defective syringe is found in the sample.- **Standard Deviation (\( \sigma \)):** Calculate the standard deviation of the distribution to understand the variability in the number of defective syringes found.This setup requires an understanding of binomial probability distributions to solve.

Answered: Image /qna-images/answer/a0dc2107-5387-477f-adc4-7c2f96ec3968.jpg

Answered: (a) Make a bar graph showing the…

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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