Suppose people immigrate into a territory at a Poisson rate of 2 per day.Assume that 40% of immigrants are adults and 60% are kids.a. What is the probability that 4 adult immigrants arrive in the next 3 days?b. What is the probability that the time elapsed between the arrival of 24thand the 25th kids is more than 2 days?c. Find mean and the variance of the time needed to have 50 adult immigrantsin the territory.

Given: X ~ Poisson(2*40%) => X ~ Poisson(0.8)

Answered: Suppose people immigrate into a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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If it is known that the percentage of successful students is 75%, and you take a sample of 15 students, calculate 1. The probability of having 10 successful bears 2. The probability of success of more than 13 students 3. variance
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4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st
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4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min
2. Doctors volunteer their time on a daily basis in a clinic. The total number of patients served in a day at the clinic has mean 90 and variance 1890. Determine the probability that 120 or more patients can be served in a day at the clinic. Use the Central Limit Theorem with continuity correction. Use linear interpolation with the normal distribution to find the probability.
Part I A bakery sells homemade bread by the loaf and sales are uniformly distributed between 200 and 600 loaves per day. a. Find the probability of selling 240 loaves on a given day. b. Find the probability of selling between 250 and 260 loaves per day Part II The golf balls produced by TruGolf have a mean distance of 250 meters and a variance of 625 meters. c. How large a sample of TruGolf balls should be taken if they want to estimate with 90% confidence the mean distance to within 8 meters? d A random sample of 40 balls from TruGolf are selected. Find the Bound of Error when the confidence level is 95% for TruGolf
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7.
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