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Consider a population which is normally distributed.If the variance of the population is 9 and n=9,what is the variance of the sampling distribution of sample means

 A line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a  standard deviation of 4 minutes. 

a. What percentage of the people in line waited for more than 20 minutes? 




Obtain the solution of the differential equation


(x^2)y" - 2xy' + 2y = (log (base e) x) ^2, (x>0),


using the method of undetermined coefficients.

Obtain the solution of the differential equation


y"+3y'+2y=e^(2t) using the method of variation of parameters

Life Insurance A 39-year-old woman purchases a $300,000 term life insurance policy for an annual payment of $450. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999053Find the expected value of the policy for the insurance companyRound to two decimal places for currency problems


A group of students got the following scores in a test:6,7,8,12,13and 15. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding mean.




State whether the following statement are true or false and also give the reason in support your answer


In a big hall there are 50 rows and each row has 60 students. A research scholar selects 10 rows randomly and then randomly selects 15; students from each selected row. It is an example of cluster sampling procedure.

State whether the following statement are true or false and also give the reason in support your answer



(1)As we increase the sample size, representativeness of the population by the sample decrease

Problem: A researcher is conducting a study about the effectiveness of a new product to the households in a certain Barangay. His population consists of the numbers 8, 4, 2, 1, 13, and 10. Let us list all possible sample size of 4 from this researcher and compute the mean of each sample.





1. Determine the number of sets of all possible random samples using the combination formula.




2. List all the possible samples and compute the mean of each sample.




3. Construct the sampling distribution.




4. Construct the histogram.

Consider a population consisting the scores of 6 students in a Statistic Test.




18, 22, 25, 28, 32, 36




Suppose samples of size 3 are drawn from this population, describe the sampling




distribution of the sample means following the steps below.





Step 4: List all possible




samples and their




corresponding means.

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