In __________, the air bags system checks itself for problems each time the ignition is turned on

I. The time till failure of an electronic component has an Exponential distribution and it is known that 10% of components have

drek231 [11]

Answer:

(a) The mean time to fail is 9491.22 hours

The standard deviation time to fail is 9491.22 hours

(b) 0.5905

(c) 3.915 × 10⁻¹²

(d) 2.63 × 10⁻⁵

Explanation:

(a) We put time to fail = t

∴ For an exponential distribution, we have f(t) = $\lambda e^{-\lambda t}$

Where we have a failure rate = 10% for 1000 hours, we have(based on online resource);

$P(t \leq 1000) = \int\limits^{1000}_0 {\lambda e^{-\lambda t}} \, dt = \dfrac{e^{1000\lambda}-1}{e^{1000\lambda}} = 0.1$

e^(1000·λ) - 0.1·e^(1000·λ) = 1

0.9·e^(1000·λ) = 1

1000·λ = ㏑(1/0.9)

λ = 1.054 × 10⁻⁴

Hence the mean time to fail, E = 1/λ = 1/(1.054 × 10⁻⁴) = 9491.22 hours

The standard deviation = √(1/λ)² = √(1/(1.054 × 10⁻⁴)²)) = 9491.22 hours

b) Here we have to integrate from 5000 to ∞ as follows;

$p(t>5000) = \int\limits^{\infty}_{5000} {\lambda e^{-\lambda t}} \, dt =\left [ -e^{\lambda t}\right ]_{5000}^{\infty} = e^{5000 \lambda} = 0.5905$

(c) The Poisson distribution is presented as follows;

$P(x = 3) = \dfrac{\lambda ^x e^{-x}}{x!} = \frac{(1.0532 \times 10^{-4})^3 e^{-3} }{3!} = 3.915\times 10^{-12}$

p(x = 3) = 3.915 × 10⁻¹²

d) Where at least 2 components fail in one half hour, then 1 component is expected to fail in 15 minutes or 1/4 hours

The Cumulative Distribution Function is given as follows;

p( t ≤ 1/4) $CDF = 1 - e^{-\lambda \times t} = 1 - e^{-1.054 \times 10 ^{-4} \times 1/4} = 2.63 \times 10 ^{-5}$ .

4 0

3 years ago

A customer executive from Southeast Asia will visit your HQ facility and meet with your

Rufina [12.5K]

Answer:

Say no!

Explanation:

Remember, this scenario is an ethical dilemma. Been ethical implies doing what's professionally right, and as such saying no to that request is the right need to do. In the workplace a company's policies should be obeyed always by individual employees even though some may resent it.

7 0

3 years ago

To embed a video using a plug-in, point to _______________ on the Insert menu and click Plugin.

babunello [35]

Answer:

d

Explanation:

8 0

2 years ago

he __________ at the bottom of the screen displays single-line help tips and displays information pertinent to the active operat

ser-zykov [4K]

The STATUS BAR at the bottom of the screen displays single-line help tips and displays information pertinent to the active operations

Explanation:

A status bar is located at the bottom of the browser window and displays the current state of the web page or application being displayed.
It is used by some applications to display helpful information for the user.
Web browsers use the status bar to display the Web address of a link when the user moves the cursor over it.
The status bar also shows the status of loading pages, and displays error messages.
A status bar is a graphical control element which poses an information area typically found at the window's bottom.
It can be divided into sections to group information together. When information is grouped it is easier to search for specific content.
The job of the status bar is primarily to display information about the current state of its window, although some status bars have extra functionality.

8 0

2 years ago

Most car owners drive their cars an average of 12,000 miles a year assuming a 20 miles a gallon gas consumption rate determine t

solniwko [45]

Answer:

9×10¹⁰ gallons

Explanation:

150×10⁶ cars × (12000 mi / car) × (1 gal / 20 mi) = 9×10¹⁰ gallons

8 0

2 years ago