Texts 4 questions circled any help is greatly appreciated 32...

Texts: 4 questions circled. Any help is greatly appreciated. 32) Find the amount of a continuous money flow in which $2000 per year is being invested at 5%, compounded continuously for 20 years. A) $68,731.27 B) $343,656.37 C) $108,731.27 D) $148,731.27 33) Determine whether the improper integral is convergent or divergent. 33) B 34) ∫f(x)e^(-x^2)dx 8 34) X 8 A) Convergent B) Divergent 35) Determine whether the function is a probability density function over the given interval. 35) A) No B) Yes 36) For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 36) f(x) = 1, [12,20] A) μ = 15.5; σ^2 = 5.20; σ = 2.28 B) μ = 16; σ^2 = 5.33; σ = 2.31 C) μ = 15; σ^2 = 5.34; σ = 2.31 D) μ = 1.6; σ^2 = 5.24; σ = 2.29 37) Let x be a continuous random variable that is normally distributed. Find the requested probability using the given mean and standard deviation. (37) The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find P(14.3 < x < 16.1) A) 0.6826 B) 0.3413 C) 0.1587 D) 0.8413

Transcript

00:05 All right, so we're told that the annual mean rates of return is standard deviation for financial assets of 10 % and 9%.

00:16 And then we're going to take 100 financial assets, and we're going to know the probability that of those 100 financial assets, that the return is less than 7%.

00:30 Now, we're only given that the mean and what the mean in standard deviation are of the population.

00:36 Because we have a large sample size n, due to the central limit theorem, which says that as long as n is greater than or equal to 30, then the distribution about the sample mean will be approximately normal.

00:49 So therefore, we can use a z score for this.

00:52 We can convert this 7 to a z score with this formula.

00:58 Z sub x bar is equal to the mean, minus the mean of the sampling distribution, which is the mean of the population.

01:06 So that's the same.

01:07 Divided by the standard error.

01:09 So the standard error, the way we calculate that is we take the population standard deviation divided by the square root of n.

01:15 So we get the mean that we're looking for is 7.

01:19 The mean of the distribution is 10.

01:22 Sigma is 9, and then root 100 here.

01:27 Great.

01:27 And then we're going to get our z score.

01:30 And right down here.

01:36 And this is what we get.

01:37 So we get the z score of negative 3 .3 repeating, which is negative 3 and 3.

01:42 And then that corresponds with the probability of 0 .00429, which as a percent would become, you know, move two decimal places over, so 0 .043%.

01:56 All right.

01:58 Then the second problem asks us about what are the assumptions of a random sample? well, first off, they have to be independent.

02:09 There's that.

02:15 And then, and that what i mean by that is that the probability of one person being selected has no impact on another person or thing being selected.

02:24 And then they also have to be mutually exclusive.

02:31 So if you're mutually exclusive, let me write that word out.

02:48 And what that means is if you're having two groups, one person or one thing can't be in both.

02:55 So you do need so you do mutually exclusive here.

02:59 And then the other piece that we need is that they have to come from the same probability distribution.

03:07 Because let's say you're sampling, let's just make something up.

03:11 Well, here we go.

03:12 Let's use our financial assets.

03:13 You're sampling the mean rates of return of financial assets and you select the hourly wage of an employee.

03:24 That's not the same probability distribution.

03:26 It doesn't, it's not there.

03:28 So they have to be in the same distribution.

03:33 And they don't have to be, you don't have to know anything about the distribution itself.

03:37 That's kind of what you're usually testing for.

03:39 I mean, sometimes you know, like we're, but we don't always.

03:43 All right.

03:44 The next part, three asks us about the default rate.

03:51 The default rate is about 8%, 8%, which is 0 .08.

03:57 And then there are 100 ,000 student loans made at this government institution.

04:05 So there's 8 % default rate on government guaranteed student loans...

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