Describe the key similarity between a binomial and a geometric distribution. O a) both distributions involve waiting times before success O b) both distributions involve counting successes c) both distributions have independent trials d) both distributions have dependent trials 国 SAMSUNG
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- 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?To correctly apply the binomial distribution, one of the conditions that that must be met is that there are only two possible outcomes. a. True O b. False O c. Cannot saySuppose that 20% of all copies of a particular textbook fail a certain bindingstrength test. Let X be the number among 5 randomly selected copies that fail thetest. Find ,the cumulative distribution function, the expectedvalues, the variance and the standard deviation
- binomial distribution For each of the following binomial distributions, compute the expected value (mean) variance and standard deviation. a) X binomial distribution with n = 20 trials; probability of success p = 0.6. b) X binomial distribution with n = 15 trials; probability of success p = 0.5. c) X binomial distribution with n = 40 trials; probability of success p = 0.8.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.q10
- 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%?The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (Hint: you can assume that the results of the two days are independent)11s
- 2)Assume that the Binomial conditions are met for the values of n and p. A fair die is thrown 10 times and getting a prime number is treated as a success. i. Find the probability of getting a prime number exactly 2 times. ii. Find the probability of getting a prime number at most 2 times. iii. Find mean, variance and standard deviation for getting a prime number.Past records indicate that the probability of online retail orders that turn out to be fraudulent is 0.08. Suppose that, on a given day, 18 online retail orders are placed, Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable. Complete parts (a) through (d) below. a. What are the mean and standard deviation of the number of online retail orders that tun out to be fraudulent? The mean number of online retail orders that turn out to be fraudulent is (Type an integer or a decimal. Round to four decimal places as needed.) The standard deviation of the number of fraudulent retail orders is. (Type an integer or a decimal. Round to three decimal places as needed.) b. What is the probability that zero online retail orders will turn out to be fraudulent? (Type an integer or a decimal. Round to four decimal places as needed.) c. What is the probability that one online retail order will turn out to be fraudulent? (Type an…Q25.If the records show that, the probability of failing (with grade F) this course is p, [use the answer of question 22 above as the probability, p, here], what is the probability that at most 2 students out of 16 fail this course? {Hint: use binomial distribution}
