According to a survey the mean student loan at graduation is...

Name: according to a survey the mean student loan at graduation is 50000 suppose that student loans are normally distributed with a standard deviation of 5000 a graduate with a student loan is sel 31106
Uploaded: 2024-02-14T00:31:06-08:00
Duration: 7 min 1 s
Channel: Taha T
Description: according to a survey the mean student loan at graduation is 50000 suppose that student loans are normally distributed with a standard deviation of 5000 a graduate with a student loan is sel 31106

According to a survey, the mean student loan at graduation is $50,000. Suppose that student loans are normally distributed with a standard deviation of $5,000. A graduate with a student loan is selected at random. Find the following probabilities. (Round your answers to four decimal places.) (a) the loan is greater than $55,000 (b) the loan is less than $47,500 (c) the loan falls between $45,000 and $56,000

Transcript

00:01 So first of all, before we sort of illustrate our distribution here, we want to denote our variable x here to correspond to the average student loan debt.

00:13 It makes things easier to sort of play around with.

00:16 We can just use x and say it's distributed, this squiggly line, this letter n, meaning normal, normal distribution, with parameters mu, which is 25 ,400, and standard deviation 12 ,050 squared, giving the variance.

00:38 Ok, so we want to find the probability that the college graduates has between 13 ,550 and 24 ,450.

00:48 Before that, however, it does ask.

00:50 We just need to comment on what mu is.

00:52 Mu is the same as the mean, which is 25 ,400.

00:58 And then part b asks for the sigma, which is the standard deviation, std dev, which is 12 ,050.

01:08 Okay.

01:11 So that was for part a, sorry.

01:14 Then for part b, we need to find this probability that i mentioned.

01:18 So probability that x lies between 13 ,550 and 24 ,450.

01:29 550.

01:31 To do this, we want to use the standard normal distribution, which is the same as taking the probability that x1 is less than mu over sigma z, and x2 is less than mu over sigma.

01:44 Here, x1 and x2 denote these two.

01:51 And we obviously know what our mu and sigma is here from the previous part of the question.

01:57 So we get this is the same as the probability that we have 13 ,550 minus 25 ,400 over 12 ,050 is less than z, which is less than 24 ,450 minus 25 ,400 over 12 ,050.

02:26 50...

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