3) A manufacturer of integrated circuits knows from experience that 5% of the components he produces aredefective. The quality control procedure is to reject an assembly-line run if three or more components out of arandom sample of ten components are defective.a) What is the probability of rejecting an assembly -line run? (Hint: Use binomial distribution formulas. It is easierto find the probability of the complement and subtract from 1)b) If X = The number of defective components in a sample size of 10, what are E(X) and o?(X) ?

A manufacturer of integrated circuits knows from experience that 5% of the components he produces…

Answered: 3) A manufacturer of integrated…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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n studies for a medication, 15 percent of patients gained weight as a side effect. Suppose 541 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that a) exactly 82 patients will gain weight as a side effect. (b) no more than 82 patients will gain weight as a side effect. (c) at least 92 patients will gain weight as a side effect. What does this result suggest? Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) P(82)= (Round to four decimal places as needed) www.
Based on long experience, an airline found that about 8% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 265 ticket reservations for an airplane with only 255 seats. (a) What is the probability that a person holding a reservation will show up for the flight? (c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)
According to the Current Population Survey (Internet Release date: September 2004), 42% of females between the ages of 18 and 24 years lived at home in 2003. (Unmarried college students living in a dorm are counted as living at home). Suppose a survey is administered today to 425 randomly selected females between the age of 18 and 24 years and 204 respond that they live at home. 1. Does this define a binomial distribution? Justify your answer 2. If so, can you use the normal approximation to binomial distribution? Justify your answer and state what the mean and standard deviation of the normal approximation are. 3. Using the binomial probability distribution, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42%? 4. Using the normal approximation to binomial, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42%?
a) If the average number of nonconforming units is 2.5, what is the probability that a sample will contain 3 or less nonconforming units? Use the Poisson distribution. b) A steady stream of income tax returns has a proportion nonconforming of 0.05. What is the probability of obtaining 3 nonconforming units from a sample of 30? Use the binomial distribution.
About 50% of all federal inmates are serving time for drug dealing. A random sample of 15federal inmates is selected.a. What is the probability that at least 12 of the inmates in the sample are serving time fordrug dealing?b. Find the expected value, variance, and standard deviation (rounded to 2 decimal places).
An article regarding interracial dating and marriage recently appeared in a newspaper. Of the 1718 randomly selected adults, 308 identified themselves as Latinos, 322 identified themselves as blacks, 253 identified themselves as Asians, and 778 identified themselves as whites. In this survey, 86% of blacks said that their families would welcome a white person into their families.NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Which distribution should you use for this problem? (Round your answers to four decimal places.) P' ~ Construct a 95% confidence interval for the population proportion of blacks that would welcome a white person into their family. (i) State the confidence interval. (Round your answers to four decimal places.) , (ii) Sketch the graph. (iii) Calculate the error bound. (Round your answer to four decimal…
A concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in the USA Today. According to the survey, 37% of adults are concerned that employers are monitoring phone calls. Use the binomial distribution formula to calculate the probability that out of five adults, exactly three are concerned that employers are monitoring their phone calls. Select one: O a. 1.85 Ob. 0.799 Oc. 0.201 d. 3.15
The proportion of items in a population that possess a specific attribute is known to be 0.25 a. If a simple random sample of size n=100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.30, what is the sampling error b. Referring to part a, what is the probability that a sample size of 100 would have a sample proportion of 0.30 or less if the population proportion is 0.25
1. The distributional pattern of pulmonate slugs inhabiting Libya was studied in the AIUB Journal of Science and Engineering (Aug. 2003). The number of slugs of a certain species found in the survey area was modeled using the negative binomial distribution. Assume that the probability of observing a slug of a certain species (say, Milax rusticus) in the survey area is 0.2. Let Y represent the number of slugs that must be collected in order to obtain a sample of 10 Milax rusticus slugs. a. Give the probability distribution for Y as a formula. b. What is the expected value of Y? Interpret this value.c. Find P(Y = 25).
About 69% of people who are murdered knew the person who committed the murder. Suppose that Detective Williams's case load currently has 49 unsolved murders. Use a nomal distribution approximation to the binomial distribution to find the following probabilities: a. What is the probability that at least 30 of the victims among Detective Williams's case files knew their murderer? b. What is the probability that between 30 and 39 of the victims knew their murderer?
1. Consider flipping a Standard US Quarter. This is an Unfair coin such that P(Tails) = 0.513 according to the best models. If you flip US Quarter 8 times you can model the number of Tails flipped as a Binomial distribution of B(8, 0.513) A. Explain why the number of Tails flipped can be modeled by this Binomial Distribution B(8, 0.513) B. What is the Expected number of Tails flipped C. What is the Expected number of Heads flipped
A poultry farmer supplies eggs to major supermarkets in Accra for sale to the general public. He claims that each crate of 30 eggs contains both brown and white eggs in a 2:1 ratio. Suppose that a randomly-selected crate of eggs has 16 brown eggs and 14 white eggs; is this observation a significant departure from the expected ratio? Take a to be 0.05.

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