A private equity firm is evaluating two alternative...

A private equity firm is evaluating two alternative investments. Although the returns are random, each investment's return can be described using a normal distribution. The first investment has a mean return of $2,000,000 with a standard deviation of $150,000. The second investment has a mean return of $2,275,000 with a standard deviation of $400,000. Complete parts a through c below. a. How likely is it that the first investment will return $1,800,000 or less? The probability is 0.0918. (Round to four decimal places as needed.) b. How likely is it that the second investment will return $1,800,000 or less? The probability is 0.1170. (Round to four decimal places as needed.) c. If the firm would like to limit the probability of a return being less than $1,650,000, which investment should it make? The probability of a return being less than $1,650,000 is nothing with the first investment and nothing with the second investment, so the firm should make the investment. (Round to four decimal places as needed.)

Transcript

00:01 They are given to invert investment here.

00:03 Let's say this is the investment one.

00:06 This is investment two.

00:08 And both of them has the normal distribution.

00:11 Let me just write the given information for the investments.

00:16 For the first one, the mean, so the mean, which is denoted by mo.

00:21 This is equal to $2 million.

00:23 So this is two times 10 to the bar of six.

00:27 And the standard deviation, which is standard.

00:30 Deviation which is denoted by sigma which is equal to 15 times so this is 15 times 10 to the power which is 4 and what about for the second one the second one is the mean this is 2 ,275 times 10 to the power which is 3 in the standard deviation which is 4 times 10 to the power 5 great.

01:08 And we can define the random variable x for this one, the normal distribution, mu and standard division.

01:13 And i can define the random variable y for the second investments, which is the mue and the standard division here.

01:20 Let's take a look at the first one here.

01:24 So the problem how the first investment will return less than this value.

01:31 So the x is less then which is 1 million this is 1 million 8 ,800 ,000 which is equal to so i'm going to use the normal cdf here the lower boundary which is negative 1 e99 the upper boundary 1 million 800 and the mean is 2 million and the standard division which is 15 1 2 3 4 great let's get the answer press second variance the second option here the lower boundary negative 1 this is 2nd e 99 and the upper boundary 18 so there are 2 4 5 zeros and this is 2 million okay this is 2 million great and the standard division which is 15 so we have 4 zeros so the answer would be which is this value here this is 0 .09 and 12 this is the answer we have for this question and the next one so for part b for the second investment, which is, so the probability of the second investment, which is 180, 800 ,000, which is again, i'm going to use the normal cdf.

03:00 So the lower boundary, this is 2, 275 and 3 zeros.

03:08 And the standard, so sorry, this is, so the upper boundary, sorry, the upper boundary is 1 ,800 ,000.

03:16 And the mean is 2 -275 -3 -0s and the standard division which is 400 ,000 let's get the answer just press second variance the normal cdf this is negative 1 second e99 and the upper boundary is 1 800 and this is 2 to 7530s and the 400 this one here so what about the probability the probability is 0 .11 and 75 great so we got this answer for the question and for part c we have to get the probability for both of them so by the way the second one should be y so the probability of random variable x which is less than this is 1 million 650 000 so this is 1 million 650 000 so i'm going to use the normal cdf and the lower boundary the upper boundary is 1650 and the mean is 2 million and the standard division 15.

04:34 Let's get the answer...

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