**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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You may need to use the appropriate appendix table to answer this question. Suppose that the average price for a gallon of gasoline in the Country A is $3.74 and in Country B it is $3.40. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the Country A and a standard deviation of $0.20 in Country B. (a) What is the probability that a randomly selected gas station in Country A charges less than $3.50 per gallon? (Round your answer to four decimal places.) (b) What percentage of the gas stations in Country B charge less than $3.50 per gallon? (Round your answer to two decimal places.) (c) What is the probability that a randomly selected gas station in Country B charged more than the mean price in the Country A? (Round your answer to four decimal places.)
The probability of a randomly selected adult in one country being infected with a certain virus is 0.004. In tests for the virus, blood samples from 30 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. The probability that the combined sample will test positive is O. (Round to three decimal places as needed.) Is it unlikely for such a combined sample to test positive? A. It is not unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is greater than 0.05. B. It is unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is less than or equal to than 0.05. OC. It is unlikely for such a combined sample to test positive, because the probability that the combined sample…
A study of immunizations among school-age children in California found that some areas have rates of unvaccinated school-age children as high as 12.5%. Let X be the number of children not vaccinated in a randomly selected classroom of 40 children in one such area? (a) what is the appropriate distribution of random variable x? (b) what is the probability that there are at most three unvaccinated children in classroom of 40? (c) what is the probability that there is at least one unvaccinated child in a classroom of 40? (d) How many unvaccinated children do we expect, on average, in randomly selected classrooms of 40 children?
Side-by-Side According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white in a 3 : I ratio. That is, cach plant has probability of having red blossoms, and the blossom colors of separate plants are independent. (c) What is the probability of obtaining at least 45 red-blossomed plants when 60 plants are grown from seeds? Use the Normal approximation. O 0.45 O 0.65 O 0.75 O 0.50
Suppose a life insurance company sells a $230,000 1-year term life insurance policy to a 20-year-old female for $220. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. Compute and interpret the expected value of this policy to the insurance company. The expected value is $ (Round to the nearest cent as needed.)
Suppose that 70% of Americans support the death penalty for persons convicted of murder. Let p> (p hat) be the sample proportion of proportion of people who support the death penalty in an SRS of Americans. Suppose we set our sample size to be n=84. What is the probability of choosing an SRS in which between 65% and 73% of the people in the people in the sample support the death penalty? That is, find P(0.65<p(phat)<0.73). Show your work and box your answer.

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