1. Refer to a 2008 report that states that 35% of US households have at least one high-definition television. Use the approximation to the binomial distribution to calculate the probability that exactly 3 of 16 randomly selected households will have at least one high-definition television
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- Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 103 people in the 18-21 age bracket and finds that 87 of them respond and 16 refuse to respond. When 267 people in the 22-29 age bracket are contacted, 235 respond and 32 refuse to respond. Assume that 1 of the 370 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who responds. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol. P(22-29 or responds) =A recent survey reported that 57% of 18- to 29-year-olds in a certain country own tablets. Using the binomial distribution, complete parts (a) through (e) below. a. What is the probability that in the next six 18- to 29-year-olds surveyed, four will own a tablet? b. What is the probability that in the next six 18- to 29-year-olds surveyed, all six will own a tablet? c. What is the probability that in the next six 18- to 29-year-olds surveyed, at least four will own a tablet? d. What are the mean and standard deviation of the number of 18- to 29-year-olds who will own a tablet in a survey of six? e. What assumption(s) do you need to make in (a) through (c)?Researchers are concerned about the rise in gun violence in their community among the adolescent population. Suppose the researchers believe that this rise in violence is due to an increase in depressive symptoms among the demographic aged 11-17. Suppose the researchers estimate that only 21% of this population suffers from depressive-like symptoms. Use a binomial distribution to solve for the following. a) What is the probability of finding no one with depressive-like symptoms in a sample of 8? b) What is the probability that at least 2 respondents of a sample of 8 report these symptoms? c) What is the expected number of adolescents in the sample to report the symptoms?
- Please show the full solution and proper notation and terminology. 3. A data firm records a large amount of data. Historically, 2% of the pages of data recorded by the firm contain errors. A sample of 300 pages is randomly selected. What is the probability that a. What is the probability that fewer than 5 pages contain errors? b. What is the probability that none of the pages contain errors? c. This binomial distribution can be approximated using Poisson if n>20 and np7. If this condition is true, the for Poisson distribution is equal to the mean for the binomial. Evaluate (a) using Poisson approximation if applicable. thanks.1. Approximately 90% of all people are right-handed. Consider a grouping of ten people. Assume that therequirements for a binomial distribution have been satisfied. a. What is the probability that 4 of them will be right handed?Approximately 90% of all people are right handed. Consider a grouping of ten people. Assume the requirements for a binomial distribution have been satisfied. a. What is the probability that 4 of them will be right handed? b. What is the probability that at least 3 of them will be right handed?
- Suppose annual expenditures on the UCI branded clothing and accessories per student are uniformly distributed between $60 and $70. A What is the probability that a student will spend more than $67? B. What is the probability that a student will spend less than or equal to $62? C. What is the probability that a student will spend between $64 and $68? D. What is the probability that a student will spend between $68 and $75? E Determine the expected spending on UCI branded clothing and accessories per student. F. Determine the standard deviation of the expenditures on UCI branded clothing and accessories per student.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?
- According to a survey, the distribution of graduate science students in doctorate-granting institutions is shown to the right. Frequencies are in thousands. A graduate science student who Field is attending a doctorate-granting institution is selected at random. Complete parts a through c. Frequency - Physical sciences 34.7 Environmental sciences 11.1 Mathematical sciences 17.5 Computer sciences Agricultural sciences Biological sciences Psychology 43.6 11.8 64.5 45.1 Social sciences 88.5 a. Determine the probability that the field of the student obtained is psychology. (Round to three decimal places as needed.)A recent study showed that 71% of adults need some type of corrective lens (glasses or contacts). A. If I grab a 6 random people what is the probability that fewer than 4 need corrective lenses? B. If I take a random sample of 2000 people what is the mean and standard deviation of the number of people who need corrective lens? C. Use the normal approximation to the binomial to find the probability that I get 1375 or fewer people who need corrective lenses out of a random sample of 2000. Illustrate what you are finding on a sketch of the normal curve and show your work.