In some experiment, two outcomes are possible: success (with probability 0.4) and failure. How many independent repetitions of this experiment are needed to conclude with probability at least 0.9 that the frequency of the height of success deviates from the probability of success in a single experiment by less than 0.1? Use: Sn (a) Bernstein's inequality (If X ~ B(n,p) then, Vɛ>0 P - ne? p>ɛ <2e4)
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- 5 The probability of success in each trial is equal to 0.25 . Using the Chebyshev-Bienaymè inequality, estimate the probability that in 800 independent trials the number of successes will be greater than 150 , but less than 250 .Q: A certain virus infects one in every 20 people. A test used to detect the virus in a person delivers positive outcome at 85% accuracy for infected persons. Moreover, it provides negative outcome for healthy persons at 95% accuracy. Compute followings: Find the probability that a person has the virus given that his test outcome is positive. Find the probability that a person does not have the virus given that his test outcome is negative. Find the probability that a person has the virus given that his test outcome is negative. Subject/Course: Introduction to Data Science Note: Use "Confusion Matrix" technique to solve this question!The probability of flu symptoms for a person not receiving any treatment is 0.025. In a clinical trial of a common drug used to lower cholesterol, 30 of 1090 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 30 people experience flu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? (a) P(X 2 30) - (Round to four decimal places as needed.)
- ) If the probability of a person getting a job is x / 3 The probability of not getting a job is 2/3 . So what is the value of xQ2: For the project, its data shown below find: ● Time in weeks that gives a probability of %97.5 Probability of finishing the project 4 weeks more than TE Probability of finishing the project 3 weeks less than TE Act. 1-2 2-3 2-5 2-4 3-4 3-7 5-6 6-7 4-7 0 8 4 7 7 4 7 10 10 4 M 10 5 8 9 6 8 14 14 5 24 12 21 11 8 15 24 24 12If the range of a given dataset(of quiz score) is 32 and and the desired number of classes is 7, then what is the class width/size of each class interval of the frequency distribution table? a. 7 b. 4 c. 4.57 d. 5
- 4 A machine consists of 300 independently operating components, each of which can fail with probability 0.6. Using Chebyshev-Beynymè's inequality, estimate the probability that the frequency of failure will deviate (in absolute value) from the probability by less than 0.05.A student will take an exam that lasts a maximum of one hour. The probability that the student finishes the exam before x hours is x / 2, 0 ≤x≤1. If it is known that the student is still taking the exam at the end of 0.75 hours, what is the probability that the student will use the entire hour?On a certain stretch of the East Coast Expressway, on average three birds per week are killed colliding with passing vehicles. The highway authority decides that if the probability of more than three birds per week being hit is more than 0.1, a special committee will be appointed to deal with the problem. Q1 (a) Determine whether the special committee will be appointed or not.
- q15A -Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…3. The amount of weight it takes to break a piece of string is normally distributed with u-22 pounds and 4 pounds. You put a weight of 18 pounds on the string. What is the probability that the string breaks? In other words, what is the probability that the weight needed to break the string is less than or equal to 18 pounds? (Hint: This is asking for Prob(-∞o << 18), which can be transformed into an inequality for z. Now think what (a) measures. You might wonder whether <0 should be included. When this is changed to z, we are looking at z <-5.5, which is negligible. See the Technical Point in the section on the normal distribution.) (Give your answer as a decimal rounded to 4 decimal places.) 0.8413 I Output: R