The mean college loan debt for graduating students at public...

Name: the mean college loan debt for graduating students at public four year institutions is 34600 with a standard deviation of 4704 if all possible random samples of size 196 are taken from this population
Uploaded: 2024-05-16T15:37:29-08:00
Duration: 12 min 22 s
Channel: Willis James
Description: the mean college loan debt for graduating students at public four year institutions is 34600 with a standard deviation of 4704 if all possible random samples of size 196 are taken from this population

The mean college loan debt for graduating students at public four year institutions is $34600 with a standard deviation of $4704. If all possible random samples of size 196 are taken from this population, determine the following: a) name of the Sampling Distribution. b) mean and standard error of the sampling distributionof the mean (use the correct name and symbol for each c) percent of GRADUATING STUDENTS for samples of size 196 that have college loan debt that is greater than $40000d) probability that sample means for samples of size 196 fall within $10,000 of the mean college loan debt for graduating students.e) Below which sample mean representing 196 graduating students can we expect to find the lowest 25% of all the sample means?

Transcript

00:01 Hello welcome to this lesson in this lesson we have the main college loan debt for graduating student at public four -year institution that is 34 600 word standard deviation of 4704 so here we are looking at possible random sample of size 186 that are taking from this population and the first part will name the sampling distribution all right so here the name of the sampling distribution is the sampling distribution of the sample mean all right now let's go to the b part where we find the mean and the standard error of the distribution of the mean so here we have the sample mean which will still be equal to the population mean and that will have the three four six zero zero and now we can look at the standard error all right that would be equals to the standard deviation of the population divided by the square root of the sample size so here we have the standard error which would be the 4704 divided by square root of 186 so we have 4704 divided by 14 supposedly or actually exactly okay you can go into it exactly exactly so we have the sample the standard error all right which is equals to three three six now let's look at the c -pad where we are looking at the percentage of graduate incident for sample of size 196 they have quality known that that is greater than 40 000 so essentially we are looking at probability that x is greater than 40 ,000 all right so convert this to z score will have x minus the mean all over the standard arrow all right so with this we'll have z which is equal to four zero zero zero zero minus the three four six zero zero divided by the three three six so here we have five four zero zero divided by three three six and we'll have a z score which is okay we have sixteen point zero seven which is so great as this call so probability that x is greater than 440 ,000 is equal to 1 minus probability that x is less than 40 ,000 using complementary probabilities right so this is also 1 minus probability that z is less than 16 0 7 alright and this probably probability that z is less than 16 .0 is one or a hundred percent plus is so greater value so we have hundred percent or let's have simply one and this goes to zero okay so so that therefore the probability that the loan amount the the loan that is greater than 40 ,000 is 0 % all right now let's go to the depart where we have so here we are looking at the probability that the sample means for the sample size of 190 196 falls within 10 ,000 of the mean college loan debt for the graduating students right so 10 ,000 it falls within 10 ,000 is 10 ,000 below the mean and 10 ,000 about the mean all right so here we are looking at probability that the mean is between 10 ,000 below it so we'll have the we have the 34600 minus 10 000 all right then we also have the 34600 plus 10 000 all right so this is the mean that we are looking for so essentially we are looking at the probability that the mean is between 24600 all right and 44600 so here we need this course needs this for one which will be the twenty four thousand six hundred minus the three four six zero zero divided by the three three six and here we have the negative ten thousand that's what we have three three six and that's negative 29 .76 which is a very key value and we have z2 which will also be the 44600 -34600 divided by the 336.

07:00 So this is also positive 29 .76.

07:08 So essentially we are looking at the probability that the mean is between these two values that is 24600 and 44600 which is essentially translating to probability that z is between negative 29 .76 and positive 29 .76 so here we write it as the probability that z is less than or equals to 29 .76 then minus probability that z is less than negative 29 .76 so here we can combine them because they are essentially of the same value so we'll have probability that z is less than 29 .76 all right minus 1 minus the the probability that z is less than 29 .76 instead of having a negative value.

08:22 Okay.

08:23 So we can have two times the probability that z is less than 29 .76, right? minus one...

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