The first digits of data entries in most real-world data sets are not uniformly distributed. The most common first digit is 1, followed by 2, and so on, with 9 being the least common first digit. This phenomenon is known as Benford's Law. The table below is the probability distribution for Benford's Law where the random variable D represents the first digit in a data entry. D P(D) D P(D) 1 0.301 6. 0.067 2 0.176 7 0.058 3 0.125 8. 0.051 4 0.097 9. 0.046 5 0.079 What is the probability that a randomly selected data entry has a first digit less than 4? P(first digit less than 4) =

A researcher gathered a sample of participants who volunteered for a studying of phobias. She measured anxiety level of participants as they viewed photos of spiders and again when they viewed puppies. Which statistical test is appropriate for this study and why?

If the odds of catching the flu among individuals who take vitamin C is 0.0342 and the odds of catching the flu among individuals not taking vitamin C is 0.2653, then the individuals not taking vitamin C are 7.7573 times more likely to catch the flu than individuals taking vitamin C.  True  False

It currently takes users a mean of 2626 minutes to install the most popular computer program made by RodeTech, a software design company. After changes have been made to the program, the company executives want to know if the new mean is now different from 2626 minutes so that they can change their advertising accordingly. A simple random sample of 5151 new customers are asked to time how long it takes for them to install the software. The sample mean is 24.924.9 minutes with a standard deviation of 2.72.7 minutes. Perform a hypothesis test at the 0.0250.025 level of significance to see if the mean installation time has changed.   Step 1 of 3 :   State the null and alternative hypotheses for the test. Fill in the blank below. H0Ha: μ=26: μ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯26

A large ski mountain has a fleet of 4 snowmobiles it uses during the winter season. It believes that the time between consecutive repair operations for a single snowmobile is an exponential random variable with a mean of .75 weeks. There are two dedicated technicians that are capable of repairing the snowmobiles. A broken down snowmobile will be repaired by one of these technicians (when one becomes available) and the repair time of a snowmobile can be modeled as an exponential random variable with a mean of .4 weeks. (a) Describe a queueing system model of the repair operations of the snowmobiles by answering the following questions: What are the customers in the queueing system? What are the servers and what service is being provided? b) Provide the rate transition diagram of the birth and death process that captures the queueing system. Be sure to provide λn and µn for each relevant value of n and your logic behind any calculations used to obtain them (c) Provide the…

Please answer all sub-parts   For a population with ? = 215 and ? = 30, what is the probability that a random sample of size 225 will have a sample mean (x bar) higher than 218?

(7) If the probability of a student graduating is 0.95, find the probability that more than 472 students students graduating among 500 students.   (8) If the probability of a student receiving financial aid is 0.72, find the mean and variance of the number of students receiving financial aid among 40000 students.   (9) There are 300 questions on a multiple choice exam. For each question there are 5 choices to choose from, and there is only one correct choice for each question. Find the mean (expected value) and variance for the number of questions you answer correctly by making random guess.

A dowser has correctly located water for a well 1 out of 2 times in Jones County. In Jones County, someone who is just guessing has a 40% chance of locating water for a well. Does this sample provide sufficient evidence that the dowser can locate water and is not just guessing?

Please show work

The proportion of drivers who use seat belts depends on things like age (young people are more likely to go unbelted) and gender (women are more likely to use belts). It also depends on local law. In New York City, police can stop a driver who is not belted. In Boston at the time of the study, police could cite a driver for not wearing a seat belt only if the driver had been stopped for some other violation. Here are data from observing random samples of female Hispanic drivers in these two cities. (a) Verify that the 95% CI for the difference in the proportions of female Hispanic drivers in the two cities who wear seat belts pNY −pBT is (0.149,0.353). Show your computation.(b) Determine if the following statements are true or false, and explain your reasoning if you identify the statement as false. i. There was strong evidence that pNY > pBT.ii. 95% of random samples of 220 female Hispanic drivers in New York City and 117 female Hispanic drivers in Boston will yield differences…