1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pentagon [3]
3 years ago
7

A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the m

ean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how many of these components must be in stock so that the probability that the system is in continual operation for the next 2000 hours is at least 0.95?
Mathematics
1 answer:
nekit [7.7K]3 years ago
5 0

Answer:

Step-by-step explanation:

From the given information:

Assuming we have an integer c to represent the components in the stocks.

Thus, the needed probability can be expressed as:

P(X_1+X_2+ ........ X_c \ge 2000)

To break this down, we have:

P(\sum X_i \ge 2000) = P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )

P \Bigg(\dfrac{\sum X_i - 100n}{\sqrt{n \ Var (X)}} \ge \dfrac{2000-100 n }{\sqrt{n \times 900}} \Bigg )= P (Z \ge 0.95 ) \ \ \  because  \ Z_{0.05} = -1.65 \\ \\  \\  \dfrac{2000-100 n }{\sqrt{n \times 900}} = -1.65 \\ \\ \\ \dfrac{100\  n-2000  }{\sqrt{900n}} = 1.65  \\ \\ 100 n -1.65 \sqrt{900 n }-2000 = 0

By solving the equation:

n = 23

Thus, relating to the needed condition; n ≥ 23

The needed number of the components that should be in stock should be  at least 23.

You might be interested in
A frustum is made by removing a small cone from a similar large cone in the diagram shown the height of a small cone is a quarte
lesantik [10]

Answer:

Volume of the frustum = ⅓πh(4R² - r²)

Step-by-step explanation:

We are to determine the volume of the frustum.

Find attached the diagram obtained from the given information.

Let height of small cone = h

height of the large cone = H

The height of a small cone is a quarter of the height of the large cone:

h = ¼×H

H = 4h

Volume of the frustum = volume of the large cone - volume of small cone

volume of the large cone = ⅓πR²H

= ⅓πR²(4h) = 4/3 ×π×R²h

volume of small cone = ⅓πr²h

Volume of the frustum = 4/3 ×π×R²h -  ⅓πr²h

Volume of the frustum = ⅓(4π×R²h - πr²h)

Volume of the frustum = ⅓πh(4R² - r²)

6 0
3 years ago
What is a commonly accepted set of assumptions
Brrunno [24]

A _______ is a commonly accepted set of scientific ideas and assumptions.

Answer: paradigm
5 0
3 years ago
Marco thinks the total number of runs a team scores in a season is a better indicator of how many wins it will have in that seas
FrozenT [24]
This is a fair assumption, but not true in every instance. Since home runs do not indicate how many runs score, which are the decider in a win or a loss, they are less accurate at predicting. 
5 0
3 years ago
Read 2 more answers
Any help would be great!
Virty [35]

Answer:

D

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
I have 4 times as much money as my brother has. our total is $55.how much does each of us have?
babymother [125]

Answer:

You have 44$, your brother has 11$.

Step-by-step explanation:

Let x be the amount of money your brother has.

Since you have four times the amount of money your brother has, we can call the amount of money you have 4x.

x+4x=55,\\5x=55,\\x=\boxed{\$11}

Thus, you have:

4(11)=\boxed{\$44}

5 0
2 years ago
Read 2 more answers
Other questions:
  • Write the equation of the line passing through the given pair of points. (-9, 7) and (-9, -1)
    15·1 answer
  • (WILL AWARD BEST ANSWER) Is the relationship shown by the data linear? If so, model the data with an equation. (Data+Choices in
    7·1 answer
  • A Circle has a circumference of 62.8 miles. What is the radius of the circle
    11·1 answer
  • It takes a boat going upstream 3 hours to cover the same distance, as it would cover in 2 hours going downstream. What is the sp
    15·1 answer
  • Graph quadrilateral abcd whose vertex matrix is shown below. Then graph the dilation of quadrilateral abcd with a scale factor o
    5·1 answer
  • (MIDDLE SCHOOL MATH) please help!
    6·2 answers
  • Find the volume of the figure.
    7·1 answer
  • PLZ IN NEED OF HELP!
    8·1 answer
  • Sin 40 cos 50 + cos 40 sin 50 find the value​
    7·1 answer
  • 4(k+1)=k+10,then 3k=<br><br>A. 3/2<br>B.5/2<br>C. 2<br>D. 6​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!