d) What is the probability that at least two different shifts will be represented among theselected workers?e) What is the probability that at least one of the shifts will be unrepresented in the sample ofworkers? Ex 1: A production facility employs 20 workers on the day shift, 15 workers on the swing shift,and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers forin-depth interviews. Suppose the selection is made in such a way that any particular group of 6 workershas the same chance of being selected as does any other group (drawing 6 slips without replacementfrom among 45).

Probability is the likelihood occurrence of the event. Possible arrangement of observation can be…

Answered: d) What is the probability that at…

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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1. The electric company owns 40 generators which power the local area. Each of these generators has a 10% chance of needing maintenance on any particular day. b) What is the expected number of generator needing maintenance on any one day? 4 40 10 400
2. The breakdown of workers in a particular state according to their political affiliation and type of job held is shown here. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Given the worker is a Democrat, what is the probability that the worker is in a white collar job. Give your answer as a decimal rounded to the nearest thousandth. Type of job 0 A. 0.472 0 B. 0.304 0 C. 0.459 Q D. 0.661 White collar Blue Collar Republican Democrat Independent 11% 17% 8% 15% 20% 29%
13.Imagine a population of balls in which all are red except for three green ones. If we randomly sample two balls, without replacement, and the probability of getting green both times is p=0.025, which of the following is the number of red balls in the population?
2. The table shows the political affiliations and types of jobs for workers in a particular state. Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted. Republican 8% Political Affiliation Independent 18% Democrat White collar 14% Type of job Blue Collar 20% 11% 29% Find the probability that the worker is a white-collar worker affiliated with the Democratic Party
6.) The National Spinal Cord Injury Statistical Center reports that 45% of all spinal cord injuries are caused by vehicle crashes. Suppose that we choose 15 spinal cord injuries at random.a.) What is the probability that 8 of the chosen injuries are from vehicle crashes? (Usethe formula)b.) What is the probability that fewer than 5 of the chosen injuries are from vehiclecrashes? (Use the calculator)c.) What is the probability that more than 9 of the chosen injuries are from vehiclecrashes? (Use the calculator)d.) What is the probability that between 4 and 10 of the chosen injuries are from vehiclecrashes? (Use the calculator)e.) What is the expected number of such injuries to result from vehicle crashes?f.) What is the standard deviation of the number of injuries resulting from vehiclecrashes?
3
3. A company produces boxes of candy that contain a mean of 50 candies each. The standard deviation is 2. Quality control will reject any box with fewer than 48 candies. a) What is the probability that a box selected at random contains exactly 51 pieces? b) What proportion of the boxes will quality control reject as containing too few candies? c) The company produces 135 000 boxes of candy a day. How many of these boxes will have at least 48 candies but no more than 53?
3. A study conducted at a large hospital found that 27.8 percent of all patients admitted to the hospital's ICU remained in the ICU for less than 24 hours. (A) If 8 patients are selected at random from the ICU patients at the hospital, what is the probability that 2 or fewer of them remained in the ICU for less than 24 hours? (B) Suppose that 20 patients are selected at random from the ICU patients at the hospital. Calculate the mean and standard deviation of the number of these patients who remained in the ICU for less than 24 hours. (C) Another result of the study was that for elective (non-emergency) admissions to the hospital's ICU, the length of the stay in the ICU had a mean of 18.9 hours and a standard deviation of 3.9 hours. Assuming that the length of stay in the ICU for elective admissions is normally distributed, what proportion of elective admissions remained in the ICU for less than 24 hours?
9. The taste test for PTC (phenylthiourea) is a common class demonstration in the study of genetics. It is know that 70% of the American population are "tasters" and 30% are "non-tasters". Suppose a genetics class of size 20 does the test to see if they match the U.S. percentages of "tasters" and “non-tasters". Assume the assignment of students to classes is a random process. a. Use the binomial expansion formula to write the expression you would use to find P(X=15 tasters) but do not evaluate the expression. Answer: b. Evaluate the expression in part a using a calculator. Answer: c. Using the notation in part a.), write out all of the probabilities need to evaluate P(X < 5 non-tasters). Use your calculator to evaluate the probability. Answer: d. Explain what probabilities you would use to evaluate P(3 < X < 9) Answer:
2. The following table shows the income distribution for two groups of people in a country: those who declare to belong to a faith, and those who declare to be free thinkers. Income bracket Middle 13278 2225 Religious outlook Faith believer Free thinker Lower 7940 1241 Upper 4527 813 (a) A person is randomly selected from the group, find the probability that this person is a (i) free thinker. (ii) free thinker given that he/she has middle income. (iii) faith believer or he/she has lower income. (b) Are the events "Free thinker" and "Middle income" independent? Explain your answer. (Note: Round the probabilities to two significant figures)
2. A container includes six components from supplier A, seven from supplier B, and eight from supplier C. What is the likelihood that each supplier will have at least one component examined if four of the components are chosen at random for testing?
4. There are 4 red balls, 6 blue balls and 2 white balls in a bag. Suppose on every single turn, you randomly select a ball, see the color of it and put it back in the bag. You keep doing this repeatedly. a. What is the probability that you get the first red ball on the 5th turn? b. How many turns are expected to get one non-white ball? c. What is the variance of the number of turns required to get one blue ball?

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d) What is the probability that at least two different shifts will be represented among the selected workers? e) What is the probability that at least one of the shifts will be unrepresented in the sample of workers?