Business weekly conducted a survey of recent graduates from...

Name: business weekly conducted a survey of recent graduates from the top mba programs on the basis of the survey assume that 50 of the recent graduates annual salary exceeds 70000 suppose you tak 03892
Uploaded: 2022-07-02T07:23:35-08:00
Duration: 6 min 53 s
Channel: Jon Southam
Description: business weekly conducted a survey of recent graduates from the top mba programs on the basis of the survey assume that 50 of the recent graduates annual salary exceeds 70000 suppose you tak 03892

Business Weekly conducted a survey of recent graduates from the top MBA programs. On the basis of the survey, assume that 50% of the recent graduates annual salary exceeds $70000. Suppose you take a simple random sample of 65 recent graduates. Note: round all z scores to 2 decimal places and all other numbers to 4 decimal places. Find the probability that more than 40% of the 65 recent graduates have an annual salary exceeding $70000.

Transcript

00:01 All right, so we have a business weekly that conducted a survey of recent grads from top mbas, mba programs.

00:08 And of the survey, we're going to assume that 60 % of recent grads had an annual salary greater than 40 ,000.

00:18 And so those we take a random sample of 51 graduates.

00:24 And the one thing to note here is we're talking about z scores.

00:29 So that's an important thing to note in all of the numbers to 4.

00:33 This one places.

00:34 So we're doing z scores here.

00:36 So find the probability that less than 70 % of the 51 recent graduates have an annual salary exceeding 40 ,000.

00:45 So this starts off as like a binomial distribution, but then we start playing around with the probability shifting around, which tells us we're probably going to be doing something with the normal distribution.

00:57 And that's one of the cool things about the binomial distribution, that you can approximate it with the normal distribution.

01:06 And so there's a few parameters.

01:09 So we look down here, we can see some of the things we need to account for.

01:15 And the thing we need to account for is right here.

01:17 These are questions for us.

01:18 And what assumptions are needed to satisfy the requirements for this problem? it says the last one here.

01:25 X is binomial, and both np and q are at least five.

01:32 That's n is the number in the sample.

01:35 So in this case, n is 51.

01:38 P is the probability, 60 % 0 .6.

01:44 And then q is 1 minus p.

01:48 Q is minus p.

01:52 So in this case, it's 1 minus 0 .6, so it's 0 .4.

01:56 And sure enough, we do.

01:58 They're both bigger than 5, both bigger than 10 even.

02:01 So that's good.

02:03 And then that allows us to approximate the binomial with the normal distribution, which is great because the normal distribution is just so lovely to work with.

02:13 I'll keep the answer there.

02:20 The way we do this is we need to find the mean in standard deviation because that's what we do with the z score.

02:26 We need to find a have an x value minus some mean over the standard deviation.

02:32 So the mean is given as n times p, so that's 30 .6.

02:37 The standard deviation is the square root of n times p times 1 minus p.

02:43 That's this number 3 .49.

02:48 We'll do 3 .5 to make it nice and easy.

02:53 But just, you know, when i did my work, i used the full precision of, i guess i would change this now and i'm looking at it.

03:06 But i was going to say i used the full precision that my spreadsheet gave me.

03:11 But we'll adjust that later on.

03:12 Okay, so we get x is this.

03:23 Oh yeah, so that's right...

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