1. Let X be a random variable that represents the wait time, in minutes, at a bank. Assume that X follows a gamma distribution with alpha = 1 and beta = 2. Find the probability that a person has to wait between 1 and 2 minutes. (Practice using the table in the book and then verify using technology.)
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- For what model are the following expressions the cumulative probability distribution for response? What is the meaning of the ; ? Pr(Y, 5 j\x)= Pr(5, S a, \x) = Pr(a + B* + + Bixu + &; < a;\x) = Pr(ɛ, sa;-a- B,xX1 -…-- B;Xx |x)If the random variable x has a Poisson Distribution with mean μ = 3.95, find the probability that x = 16.The mean percent of childhood asthma prevalence in 43 cities is 2.11%. A random sample of 30 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.6%? Interpret this probability. Assume that o = 1.35%. The probability is. (Round to four decimal places as needed.)
- A health and safety consultant working in a large department store finds that the wait time for a lift on the second floor of the building can be modelled with a continuous uniform distribution ranging from 1 to 5 minutes. The lift takes 30 seconds to move from one floor to the next. Calculate the probability that a person can reach the ground floor in less than 2.25 minutes after pushing the button to request the lift on the second floor.Assume that the number of episodes per year of otitis media, a common disease of the middle ear in early childhood follows a Poisson distribution with 2.7 episodes per year. What is the probability of having at most 2 episodes in the first year of life? (Approximate your answer to 4 decimal places). NB: You must follow instructions on how to approximate the answer, or your work will be marked as incorrect.The probability distribution itself is assumed to be a beta distribution. True or false?
- The mean percent of childhood asthma prevalence in 43 cities is 2.21%. A random sample of 32 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.6%? Interpret this probability. Assume that o= = 1.21%. The probability is (Round to four decimal places as needed.)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.…Looking at the ABC company Cat Kibbles data set, the quality manager of that company selects and stores two samples per year from the manufacturing line to do quality checks on. This means that over the period of three years from 2014 to 2016, she selected 6 samples in total, to do testing on. Calculate the probability of a success. Provide this answer to 4 decimal points. Do not use a comma. Use only a period (.) to indicate your decimal