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(1) A local ice-cream store receives an average of 3 customers per hour. Assume that the arrival events are well described by Poisson distribution. The cashier wants to leave the store to run an errand. The manager computes the expected time T between the arrivals of consecutive customers over the previous week and allows the cashier to leave the store for a duration T. How long does the cashier have to run his errand? Hint: If the occurrence of events is described by Poisson distribution, then the inter-event time is described by exponential distribution. (2) A basketball player can score a basket on fifth attempt, on an average. What is the probability that the player scores the third basket on the tenth attempt? Hint: Sum of geometric random variables is a negative binomial random variable. (3) A sump pump in a basement has two battery-operated back-up pumps. In the case of power outage the main sump pump shuts off and the first battery-operated back-up pump kicks in. After the battery powering the first back-up pump runs out of charge, the second battery-operated back-up pump is activated. Assume that the duration for which a battery can power its pump is described by expo- nential distribution. The variation in the time the battery lasts is due to the variation in the rate of accumulation of ground water. A battery can power its pump for 20 minutes on an average, before it runs out of charge. A certain power outage lasts an hour. What is the probability that the basement will not get flooded during the power outage? Hint: You will need to use the Gamma distribution. The integral involved is simple. Γ(n + 1) = n! if n is a non-negative integer.
Find the 96th percentile of the distribution of reaction time (at least approximately). That is, find the value such that about 96% of the distribution is below this point - Find the probability the reaction time is 500 or less.
A screening test for a newly discovered disease is being evaluated. In order to determine the effectiveness of the new test, it was administered to 900 workers; 150 of the individuals diagnosed with the disease tested positive.
Please read through the case scenario shown below to gain an understanding of the background information and the research study
What is the latest possible time that Activity E can be started without delaying the completion of the project and what is the latest time that activity B can start without delaying the project
What is Goldbergs rationale for the study? Was the study designed to contribute to theory? Do the results of the study contribute to theory and how does a multiple-baseline design differ from a reversal design?
Perform exploratory data analysis on the relevant variables in the dataset. When possible, include appropriate graphs to help illustrate the dataset.
Evaluate the correlation coefficient.
Determine whether this data already provides an expected relative error introduced by the simulation of below 5%. If not, compute how many new simulations you should run in order to reduce the expected relative error introduced by the simulation b..
Complete the analysis of variance. At a .05 level of significance, is there a significant difference between the treatments?
What is the difference in proportions in the original data and what is the p-value and what does it mean in terms of this specific problem
Analyze the processed data in Statistical survey.
There evidence that the mean price is higher at Whole Foods Market than at the Fairway supermarket and interpret the meaning of the p-value in (a)
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