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THERE !!✨,
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Answer: 53
Step-by-step explanation:
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Step-by-step explanation:
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A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.5 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely.
A. For how many months should the satellite be insured to be 94% confident that it will last beyond the insurance date?
B. If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends?
C. If the satellite is insured for 84 months, what is the expected loss to the insurance company?
D. If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make?
Answers
Answer:
a) The insurance should be of 84.6 months, that is, approximately 85 months.
b) 0.0436 = 4.36% probability that it will malfunction before the insurance coverage ends.
c) The expected loss to the insurance company is of 2.18 million.
d) The company should expect to make a profit of $689,200.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
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.
A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.5 months.
This means that [tex]\mu = 90, \sigma = 3.5[/tex]
A. For how many months should the satellite be insured to be 94% confident that it will last beyond the insurance date?
The 100 - 94 = 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 90}{3.5}[/tex]
[tex]X - 90 = -1.555*3.5[/tex]
[tex]X = 84.6[/tex]
The insurance should be of 84.6 months, that is, approximately 85 months.
B. If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends?
This is the pvalue of Z when X = 84. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z= \frac{84 - 90}{3.5}[/tex]
[tex]Z = -1.71[/tex]
[tex]Z = -1.71[/tex] has a pvalue of 0.0436
0.0436 = 4.36% probability that it will malfunction before the insurance coverage ends.
C. If the satellite is insured for 84 months, what is the expected loss to the insurance company?
0.0436 probability of losing 50 million. So
0.0436*50 = 2.18
The expected loss to the insurance company is of 2.18 million.
D. If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make?
1 - 0.0436 = 0.9564 probability of making 3 million.
0.0436 probability of losing 50 million
So
[tex]E = 0.9564*3 - 0.0436*50 = 0.6892[/tex]
The company should expect to make a profit of 0.6892 million, that is, $689,200.
1/3 How many minutes does April jump rope 1 day? 1 week. Please tell the answer for 1 day and 1 week
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Answer:
1/3
i don't know laughing out loud
What kind of angels are 1 and 2 ?
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Can someone please help
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Answer:
6^7
Step-by-step explanation:
6^8 x 6^-1
6^{8-1}
6^7
What is the value of x in the equation 0.7x -1.4 = -3.5?
O-7
0-3
O 3
O 7
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Explanation: To find any value of x, you have to get it alone. As -1.4 is being subtracted from 0.7x, you’d do the opposite of the order of operation that it’s doing. So because -1.4 is negative, (being subtracted), you’d have to add -1.4 on both sides of the equation to eliminate the -1.4 from being near the 0.7x. You’re then left with 0.7x = -3.5 + 1.4
You then add those up (-3.5 + 1.4) giving you (-2.1) as your final answer and you’re left with 0.7x = -2.1. You then divide 0.7 from both sides to get x alone, leaving you with -3 as your final answer!
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hlpppp meee hshshdjdjdj
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Answer:
its b
Step-by-step explanation:
I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS
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Answer:
5150
Step-by-step explanation:
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The circumference of the equator of a sphere was measured to be 82 82 cm with a possible error of 0.5 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area to 4 decimal places.
Answers
Answer:
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
Step-by-step explanation:
The circumference ([tex]s[/tex]), in centimeters, and the surface area ([tex]A_{s}[/tex]), in square centimeters, of a sphere are represented by following formulas:
[tex]A_{s} = 4\pi\cdot r^{2}[/tex] (1)
[tex]s = 2\pi\cdot r[/tex] (2)
Where [tex]r[/tex] is the radius of the sphere, in centimeters.
By applying (2) in (1), we derive this expression:
[tex]A_{s} = 4\pi\cdot \left(\frac{s}{2\pi} \right)^{2}[/tex]
[tex]A_{s} = \frac{s^{2}}{\pi^{2}}[/tex] (3)
By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area ([tex]\Delta A_{s}[/tex]), in square centimeters:
[tex]\Delta A_{s} = \frac{\partial A_{s}}{\partial s} \cdot \Delta s[/tex]
[tex]\Delta A_{s} = \frac{2\cdot s\cdot \Delta s}{\pi^{2}}[/tex] (4)
Where:
[tex]s[/tex] - Measure circumference, in centimeters.
[tex]\Delta s[/tex] - Possible error in circumference, in centimeters.
If we know that [tex]s = 82\,cm[/tex] and [tex]\Delta s = 0.5\,cm[/tex], then the maximum error is:
[tex]\Delta A_{s} \approx 8.3083\,cm^{2}[/tex]
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
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Rearrange this equation that "0" is the subject.
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The table shows the pricing for four different types of apples.
Which type costs the least per kilogram?
A $4 for 1.5 kg
B $5 for 2.0 kg
C $7 for 2.5 kg
D $8 for 3.5 kg
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What is the value of x?
• 12 units
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O 20 units
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Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Please help me click the picture to see
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Factoring:
Convert 0.25 to a fraction:
1/4x+97
Factor out 1/4:
Solution:
1/4(x+388) or 0.25(x+388)
1.5 x 10 to the power of 11
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Answer:
150000000000
Step-by-step explanation:
1.5x10¹¹
= 150000000000
You can think about scientific notations by moving the position of the 'dot' 11 times to the right
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ABC is a right-angled triangle.
Calculate the area of the circle.
Give your answer correct to 3 significant figures. *
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Answer:
area is approximately 36.56
Step-by-step explanation:
The width of a pool is x meters long. The length of the pool is four meters longer than the width. Using this information, state the width and length on the area diagram of this pool.
Write answer in simplest standard form.
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Answer:
Width = ×
Length = × + 4
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Answer:
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Step-by-step explanation:none.
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Answer:
[tex] {x}^{2} + 2xy + {y}^{2} [/tex]
Step-by-step explanation:
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Answer:
x= 25.6 (nearest tenth)
Step-by-step explanation:
Please see the attached picture for the full solution.
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Answer:
$82.50
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
already in order
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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You have 50 cups. 10 cups are blue, 20 cups are red, and 20 cups are white. What percentage of cops are blue?
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Answer:
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Step-by-step explanation:
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The comparative statements of Wahlberg Company are presented here.
Wahlberg Company
Income Statement
For the Years Ended December 31
2020
2019
Net sales
$1,817,500 $1,753,100
Cost of goods sold
1,008,600 978,000
Gross profit
808,900 775,100
Selling and administrative expenses
519,200 480,800
Income from operations
289,700 294,300
Other expenses and losses
Interest expense
18,900 14,100
Income before income taxes
270,800 280,200
Income tax expense
81,512 78,000
Net income
$ 189,288 $ 202,200
Wahlberg Company
Balance Sheets
December 31
Assets
2020
2019
Current assets
Cash
$60,300 $64,500
Debt investments (short-term)
68,300 50,500
Accounts receivable
116,100 101,000
Inventory
122,700 115,200
Total current assets
367,400 331,200
Plant assets (net)
603,300 521,600
Total assets
$970,700 $852,800
Liabilities and Stockholders’ Equity
Current liabilities
Accounts payable
$161,000 $145,900
Income taxes payable
43,100 41,900
Total current liabilities
204,100 187,800
Bonds payable
220,000 200,000
Total liabilities
424,100 387,800
Stockholders’ equity
Common stock ($5 par)
276,200 297,400
Retained earnings
270,400 167,600
Total stockholders’ equity
546,600 465,000
Total liabilities and stockholders’ equity
$970,700 $852,800
All sales were on account. Net cash provided by operating activities for 2020 was $240,000. Capital expenditures were $146,000, and cash dividends were $86,488.
Compute the following ratios for 2020. (Round Earnings per share, Current ratio and Asset turnover to 2 decimal places, e.g. 1.65 or 1.65:1, and all other answers to 1 decimal place, e.g. 6.8 or 6.8%. Use 365 days for calculation.)
(a)
Earnings per share
$enter your answer rounded to 2 decimal places
(b)
Return on common stockholders’ equity
enter your answer rounded to 1 decimal place
%
(c)
Return on assets
enter your answer rounded to 1 decimal place
%
(d)
Current ratio
enter your answer rounded to 2 decimal places
:1
(e)
Accounts receivable turnover
enter your answer rounded to 1 decimal place
times
(f)
Average collection period
enter your answer rounded to 1 decimal place
days
(g)
Inventory turnover
enter your answer rounded to 1 decimal place
times
(h)
Days in inventory
enter your answer rounded to 1 decimal place
days
(i)
Times interest earned
enter your answer rounded to 1 decimal place
times
(j)
Asset turnover
enter your answer rounded to 2 decimal places
times
(k)
Debt to assets ratio
enter your answer rounded to 1 decimal place
%
(l)
Free cash flow
$enter your answer in dollars