2. Suppose it is claimed that amongst the population of STM1001students, the number of items bought online in the past year is normallydistributed with a mean of u20 and variance of o2 = 25. Furthersuppose that we wish to study the mean of the population by taking arandom sample of n = 61 STM1001 students. Using this information,write down the distribution of the sample mean, X. Note: In each box,enter a single number rounded to four decimal places where relevant. (2marks) X~ N( 200.409824. Again following on from the previous question, what is the probabilitythat when we take a random sample of n = 61 STM1001 students, thesample mean would be either greater than 20.3521 or less than19.6479? [int.orty will bown that

given data ,normal distributionμ=20σ2=25n=61here we have to find out the value of mean and standard…

Answered: 2. Suppose it is claimed that amongst…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Ex. Derive the MLE for a random sample from Exp(A) distribution that is subject to left truncation and right-censoring (LTRC); be sure to provide its variance estimate as well. Compare to the case where there is only right-censoring that we derived in the lecture notes earlier.
The Human Resources Director of a central hospital wishes to estimate the mean number of children admitted to the pediatric clinic during a day. The director randomly selects 64 different days and determines the number of admissions for each. Based on this sample, she computes the sample's arithmetic mean X-bar = 19.8 and the sample's variance S2 = 36. You are requested to calculate the sample size that the director should choose if she wishes to estimate the mean number of admissions per day to within ±1 admission with a 95% level of confidence? Note: You can use the sample standard deviation as an estimate for the population standard deviation. A. 97 B. 68 C. 98 D. 139 E. 239
Suppose that the average salary of health systems professionals is normally distributed with µ=KES 40,000 and σ = KES 10,000. What proportion of professionals will earn KES 24,800 or less? What proportion of professionals will earn KES 53,500 or more? What proportion of professionals will earn between KES 45,000 and KES 57,000? Calculate the 80th percentile. Calculate the 27th percentile
Suppose that the City of Chicago is interested in potential revenues if they introduce a tolling station near O'Hare. Further suppose that the average time between cars is only 2.4 seconds; what is the variance of the distribution?
can you fill in the blanks
Suppose that random samples of size 36 are repeatedly drawn from a populationwith mean 28 and standard deviation 9. Describe the sampling distribution of X¯. NOTE: Please explain each part, so the problem can be used as a Study Guide
Suppose a batch of steel rods produced at a steel plant have a mean length of 187 milimeters, and a Variance of 64. If 416 rods are sampled at random from the batch, what is the probability that the mean length all the sample rods would differ from the population mean by less than 0.65 millimeters? Round your answer to four decimal places.
Suppose the number of off springs a female eagle raises during its lifetime has a distribution with mean 15 and variance 4. In an area, 45 rescued and cured female eagles are set free. If these eagles are assumed to be independent (no lack of male partners and food resources), the total number of off-springs produced by these eagles can be assumed to have a Normal distribution with mean and variance
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
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
When using analysis of variance , the calculated F statistic will decrease as A) the variability among the groups decreases relative to the variability within the groups.B) the total variability increases.C) the total variability decreases.D) the variability among the groups increases relative to the variability within the groups.
A researcher takes sample temperatures in Fahrenheit of 20 days from Minneapolis and 18 days from Cleveland. Use the sample data shown in the table. Test the claim that the mean temperature in Minneapolis is different than the mean temperature in Cleveland. Use a significance level of α=0.01. Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs. Minneapolis Cleveland 70.1 66.1 69.5 65.9 65.7 61 71.7 62.8 62 67.9 75.3 74.5 63.2 69.1 62 72.5 76.9 80.4 71.3 72.7 70.9 70.4 70.5 76.6 65.1 62.2 76.2 66.1 70.3 86 69.5 81 80.2 68.3 74.3 63.3 70.7 64.6 The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2 Based on these hypotheses, find the following. Round answers to 4 decimal…

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