Consider a company that has two different divisions. The annual profits from the two divisions are independent and have distributions Profit1 ~ N(5, 3^2) and Profit2 ~ N(7, 4^2) respectively. Both the profits are in $ Million. Assume that $1 = Rs. 45
A. Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.
B. Specify the 5th percentile of profit (in Rupees) for the company
C. Which of the two divisions has a larger probability of making a loss in a given year?
Answers
Answer:
a) Rs 603.68
b) Rs 476.33
c) first division
Step-by-step explanation:
Total profit = profit 1 + profit 2 = P
hence P ~ N(12,74) = [tex]\frac{P-12}{\sqrt{74} } ~ N(0,1)[/tex]
A ) Specifying a Rupee range ( centered on the mean ) that contains 95% probability for annual profit of the company
$13.41 = Rs 603.68
B) specifying the 5th percentile of profit
p = $10.59 ≈ Rs 476.33
C) The division that has a larger probability of making a loss in a given year is the first division
attached below is a detailed solution of the given problem
A): Range containing 95% probability for profit of company is
(Rs. 99M, Rs. 1026M).
B): Rs. 170.1 Million.
C): First division of the company has larger probability of making a loss.
Given that:
$1 = Rs. 45
[tex]Profit_1 \sim N(5, 3^2) \\ Profit_2 \sim N(7, 4^2)[/tex]
Thus,
Company's profit:
[tex]P \sim N( 5+7, 3^2 + 4^2) = N(12, 5^2)[/tex]
A):
95% of the probability lies between 1.96 standard deviations of the mean.
Thus range is:
[tex]= (12 - 1.96\times 5, 12 + 1.96 \times 5)\\\\= (\$2.2M, \$22.8M)\\ \\= (\rm Rs. \: 99M, \rm Rs. \: 1026M)[/tex]
B): Fifth percentile is calculated as:
[tex]P(Z \leq \dfrac{p-12}{5}) = 0.05[/tex]
From p values of z score table, we get:
[tex]\dfrac{p-12}{5} = -1.644\\p = 12 - 8.22 = 3.78\\[/tex]
Thus at $3.78M dollars, or Rs. 170.1M amount, 5th percentile of profit lies.
Or 5th percentile of profit is Rs. 170.1 Million.
C): Loss is when profit < 0
Thus: p < 0
The first division of company, thus have larger probability of making a loss in a given year.
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Related Questions
Look at the table.
Cars Sold
Annual Bonus
120
$1,800
130
$1,950
150
$2,250
175
$2,625
What is the annual bonus for a salesperson who sells 55 cars?
$150
$825
$1,500
$8,250
Answers
Answer: $825 (B)
Step-by-step explanation:
it’s obvious
Answer: The answer is B!
Step-by-step explanation: It's on edge, hope this helped!
How many proper subsets does the set T= {x,y,z} have?
Answers
Answer:
Total Proper Subsets = 2ⁿ - 1 = 2³ -1 =8-1 =7
Step-by-step explanation:
Basically the formula for,
No of subsets = 2ⁿ
Where n is number of elements in a set. As one subset is improper which is equal to the set itself so we have to find proper subsets which are = 2ⁿ - 1.
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For which pair of points can you use this number line to find the distance?
4
2 3
5 6
-2 -1 0 1
7 8
(-4, 1) and (7,4)
(-4, 1) and (-4,7)
(-1, 4) and (4,7)
O (-4, -1) and (-4,-7)
Answers
Answer:
[tex](-4, 1) \: and \: (-4,7)[/tex]
Step-by-step explanation:
[tex]the \: shortest \: distance \: between \: two \: points \: can \: be \: used \: here \to \\ were : d = \sqrt{ (x_{2} -x_{1} ) {}^{2} + (y_{2} -y_{1} ) {}^{2} } \\checking \: for \: the \: pair \to \: (-4, 1) \: and \: (-4,7) \\ d = \sqrt{ (( - 4)-( - 4)) {}^{2} + (7 -1 ) {}^{2} } \\ d = \sqrt{ (- 4 + 4) {}^{2} + (6) {}^{2} } \\ d = \sqrt{ (0) {}^{2} + (6) {}^{2} } \\ d = \sqrt{ (6) {}^{2} } \\ \underline{ \boxed{d = 6}}[/tex]
Plz help due tomorrow
Answers
Answer:
Step-by-step explanation:
1/6 x 1/5 + 1/30
= 1/30 + 1/30
= 2/30
=1/15
It is asking us to plug in 1/5 so let’s plug it in
1/6(1/5) + 1/30 = 1/30 + 1/30 = 2/30
So we reduce the fraction and the answer is 1/15
what is -X - 29 = 15 - 3x
Answers
Answer: x = 22
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x =22
Step-by-step explanation:
Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3,100. Assume that the standard deviation is $1,400.
Required:
a. What is the z-score for a backyard structure costing $2300?
b. What is the z-score for a backyard structure costing $4900?
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.
Answers
Answer:
a) The z-score for a backyard structure costing $2300 is -0.57.
b) The z-score for a backyard structure costing $4900 is 1.29
c) A backyard structure costing $2300 costs 0.57 standard deviations below the mean, while a backyard structure costing $4900 costs 1.29 standard deviations above the mean. Since both are within 2 standard deviations of the mean, none is an outlier.
d) Since this combination costs more than 2 standard deviations from the mean, yes, it should be considered an outlier.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If the z-score is more than two standard deviations from the mean(lesser than -2 or more than 2), the score X is considered an outlier.
In this question, we have that:
[tex]\mu = 3100, \sigma = 1400[/tex]
a. What is the z-score for a backyard structure costing $2300?
We have to find Z when [tex]X = 2300[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2300 - 3100}{1400}[/tex]
[tex]Z = -0.57[/tex]
The z-score for a backyard structure costing $2300 is -0.57.
b. What is the z-score for a backyard structure costing $4900?
We have to find Z when [tex]X = 2300[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4900 - 3100}{1400}[/tex]
[tex]Z = 1.29[/tex]
The z-score for a backyard structure costing $4900 is 1.29
c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.
A backyard structure costing $2300 costs 0.57 standard deviations below the mean, while a backyard structure costing $4900 costs 1.29 standard deviations above the mean. Since both are within 2 standard deviations of the mean, none is an outlier.
d. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier?
We have to find the z-score when X = 13000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13000 - 3100}{1400}[/tex]
[tex]Z = 7.07[/tex]
Since this combination costs more than 2 standard deviations from the mean, yes, it should be considered an outlier.
34) Which equation is equivalent to: 3r=78+14 ?
A. −3r=−78+14
B. 3r−14=78
C. 3r=78−14
D. −3r=78−14
Answers
Solve.
How much pure acid is in 860 milliliters of a 18% solution?
The answer is ____ ml.
Answers
Answer:
The answer is 154.8 ml
Step-by-step explanation:
In this question, the amount of pure acid is 18% of the total solution, that is, 18% of 860 milliliters. So
0.18*860 = 154.8 ml
The answer is 154.8 ml
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Connor is working two summer jobs, making $8 per hour walking dogs and making $12 per hour landscaping. In a given week, he can work a maximum of 15 total hours and must earn no less than $160. If Connor worked 12 hours walking dogs, determine the maximum number of whole hours landscaping that he can work and still meet his requirements. If there are no possible solutions, submit an empty answer.
Answers
Answer:
[tex]\mathrm{No\: solutions}[/tex]
Step-by-step explanation:
Since Connor has worked 12 hours walking dogs, he's earned [tex]12\cdot 8 = \$96[/tex] from walking dogs. He still needs to earn [tex]\$160-\$96=\$64[/tex]. As stated in the problem, he makes $12 an hour landscaping, therefore the minimum number of whole hours he must work to fulfill his requirements is [tex]\lceil{ \frac{64}{12} \rceil = 6\: \mathrm{hours}[/tex]. However, the problem states he can only work a maximum of 15 hours. He would have to work [tex]12+6=18[/tex] to fulfill his requirements and therefore he will not be able to meet his requirements with the restrictions given.
solve for x x−6/9=−5
x=
Answers
Answer:
4 4/9
Step-by-step explanation:
Move all terms not containing x
to the right side of the equation.
Exact Form:
x=−409
Decimal Form:x=−4.¯4
Mixed Number Form:
4 4/9
Answer:
-39
Step-by-step explanation:
x-6/9 = -5
then multiply both sides by 9
9 ° (x-6) / 9 = 9 ° -5
simplify
x-6= -45
add 6 to both sides
x-6+6=-45+6
simplify
x= -39
Someone help me quick
Answers
Answer: x > - 18
Step-by-step explanation:
first multiply both sides
then multiply reduce
then arrange and thats the answer
hope this helps <3
How do I do this -16x =-160
Answers
Answer:
you have to put -160 over -16 then divide and your answer will be 10
so x=10. I hope this helps :)
solve the question below, please
Answers
Answer:
carios has greater angle
Step-by-step explanation:
hope this helps
The sum of four times a number and fifteen is forty-seven. Find the number.
Answers
Answer:
8 is the number
Step-by-step explanation:
I don't know why it took me so long to figure it out, 4 x 8 = 32 32 + 15 = 47
It probably took me a really long time because I am tired, and I am not using a calculator.
PLEASE HELP ME i rly need an a
what is how much sales tax will Larry pay for his $939 doorbell in Las Vegas, where the sales tax is 8.38%? Use appropriate units and round your answer to the nearest cent if necessary. * plez i beg
Answers
Answer:
939/x 8.38/100
x8.38 93900
x= 11205.25
Step-by-step explanation:
Four sisters are all 2 years apart in age. The
total of their ages is equal to 36 years. How
old is the youngest sister
Answers
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The four sisters are all 2 years apart in age. The total of their ages is equal to 36 years.
Let x be the age of the youngest sister. Then the age of other sister will be x + 2, x + 4, and x + 6. Then the equation is given as,
x + x + 2 + x + 4 + x + 6 = 36
4x + 12 = 36
4x = 36 - 12
4x = 24
x = 24 / 4
x = 6
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
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https://brainly.com/question/953809
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HELP !!!! find the measurements of each angle
Answers
If three pounds of bananas cost $4.50 find the cost of 10 pounds of bananas
Answers
Answer:
45
Step-by-step explanation:
4.50 × 10 =45!
.
.
.
.
.
.?
.
.
.
.
.
Answer:
$15
Step-by-step explanation:
$4.50 time 3 = $13.50 (9 lbs)
$4.50 divided by 3 = $1.50 (1 lb)
$1.50 plus $13.50 = $15
1. Line L passes through point (-1, 2) and (-3,-2) on a coordinate plane. Line
M passes through the points (1.1) and (-1, W). For what value of W will make
line L and line M parallel.
Answers
Answer:
Slope of a line passing through ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2} , y_{2}[/tex]) is given by:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Now,
Slope of line L, (m) = [tex]\frac{-3-(-1)}{-2-2}[/tex] = 0.5
Slope of line M, (n) = [tex]\frac{-1-1}{W-1}[/tex] = [tex]\frac{-2}{W-1}[/tex]
If the lines L and M are parallel to each other,
m = n
or, 0.5 = [tex]\frac{-2}{W-1}[/tex]
or, 0.5 (W - 1) = -2
or, W - 1 = -4
or, W = -3
Therefore the required value of W is -3.
Find the value of x.
92°
36°
Answers
Answer: the answer is 7°
Step-by-step explanation:
The test scores of students in a math class are 56, 42, 50, 63, 58, 41, 50, 48, 68, and 48. What is the mean of this set of data?
A. 55.6
B. 50
C. 52.4
D. 48.6
Answers
(1) 56 + (2) 42 + (3) 50 + (4) 63 + (5) 58+ (6) 41 + (7) 50 + (8) 48 + (9) 68 + (10) 48 = 524
524/10 = 52.4
Answer:
C. 52.4
Step-by-step explanation:
Y-4x=9 in standard form please show your work
Answers
Answer:
y = x + 9/4 or y = x + 2 1/4
Step-by-step explanation:
y - 4x = 9
y - x = 9/4 (divide both sides by 4)
y = x + 9/4 (Add x to both sides)
Express the reoccurring decimal 0.56 as a fraction
Please see screenshot
Answers
Answer:
I have made it in pic hope it helps
Dean purchased a box of cereal Which of these measurements BEST describes the volume of the box?
1.)154 cubic feet
2.)154 cubic inches
3.)154 cubic meters
4.)154 cubic millimeters
Answers
Answer:
2
Step-by-step explanation:
You don't measure cereal in the others because feet, meters and millimeters are too big. Hope this helps.
Simplify
6(-5n + 7 thank you
Answers
Answer:
-30n + 42
Step-by-step explanation:
6( -5n + 7)
-30n + 42
Hope this helps!
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Determine if the two triangles are congruent. If they are, state how you know.
Answers
Answer:
There is not enough information to say they are congruent
Step-by-step explanation:
To prove two triangles are congruent, you need 3 things, which you can see through the list of options you were given. But since we only have two, there isn't enough information to prove the are congruent.
Jane drove 693 miles in 11 hours.
At the same rate, how long would it take her to drive 411 miles?
Answers
Answer:
approx. 6.523809523809524 hours
Step-by-step explanation:
Let us first find how long it takes Jane to drive 1 mile.
11/693 = approx. 0.015873015873016 hours to drive one mile.
She drives 411 miles, so we can multiply that by 411:
0.015873015873016 * 411 = approx. 6.523809523809524 hours
I hope this helps! :)
Answer:
6.52 hours
Step-by-step explanation:
693 miles divided by 11 hours = 63 miles per hour.
411 miles divided by 63 miles = 6.52380952 miles
Round to 2 decimal places: 6.52 hours
Simplify the following expression (2x^2y^5)^3
Answers
Answer:
The correct answer is,
[tex] {8x}^{6y {}^{5} } [/tex]
Question 5 (1 point)
Find the area of the shaded region of this regular polygon. (Round to the nearest
hundredth)
Answers
Height of triangle = 4tan(67.5°)
area of triangle = 0.5(base)(height) = 0.5(8)(4tan(67.5°))
Shaded region = 2*0.5(8)(4tan(67.5°)) = 32tan(67.5°) ≅180.71 cm^2
Item 7
The ratio of the weight of an object on Jupiter to its weight on Earth is 8:5, meaning that an object that weighs 8 pounds on Jupiter weighs only 5 pounds on Earth. In the first box provided, write an equation that represents the relationship between the weight on Jupiter j and the weight on Earth e and on the second line, write its reciprocal.
Answers
Answer:8,5 recirpoal is 5,8
Step-by-step explanation: