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
MaRussiya [10]
3 years ago
9

A complicated mechanical system contains 8 components. If there is a 18% chance that each component will fail during processing,

and components fail independently of each other, then
(a) What is the probability that fewer than 3 components will fail?
(b) What is the meet likely number of failures?
Mathematics
1 answer:
kicyunya [14]3 years ago
3 0

Answer:

(a) The probability that fewer than 3 components will fail is  0.8392.

(b) The mean likely number of failures is 1.44.

Step-by-step explanation:

We are given that a complicated mechanical system contains 8 components. If there is an 18% chance that each component will fail during processing, and components fail independently of each other.

Let X = <u><em>Number of components fail during processing</em></u>

The above situation can be represented through the binomial distribution;

P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,.....

where, n = number of samples (trials) taken = 8 components

            r = number of success = fewer than 3 components will fail

           p = probability of success which in our question is the probability

                 that each component will fail during processing, i.e. p = 18%

SO, X ~ Binom(n = 8, p = 0.18)

(a) The probability that fewer than 3 components will fail is given by = P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= \binom{8}{0}\times 0.18^{0} \times (1-0.18)^{8-0}+ \binom{8}{1}\times 0.18^{1} \times (1-0.18)^{8-1}+ \binom{8}{2}\times 0.18^{2} \times (1-0.18)^{8-2}

= 1 \times 1 \times 0.82^{8}+ 8 \times 0.18^{1}  \times 0.82^{7}+28 \times 0.18^{2}  \times 0.82^{6}

= <u>0.8392</u>

(b) The mean likely number of failures is given by the following formula;

      Mean of X, E(X) = n \times p

                                 = 8 \times 0.18 = 1.44

Hence, the mean likely number of failures is 1.44.

You might be interested in
Given the vectors w = &lt;-5, 3&gt; and z = &lt;1, 4&gt;, find the results of the vector subtractions.
Alex

Answer:

Given two linearly independent vectors w and z

We want -w-z

Hence apply a negative gradient to w

w=-<-5,3> =<5,-3>

So <5,-3>-<1,4> = (<5-1>,<-3-4>)

The answer is <4,-7>

6 0
2 years ago
HELP PLEASSEE
Marizza181 [45]
The diameter is 4 inches.
6 0
3 years ago
What is the result of 40-16\4
viva [34]

If the question is 40 - \frac{16}{4} , then you would do 16 ÷ 4 = 4, and then 40 - 4 = 36.


If the question is \frac{40 - 16}{4} , then you divide both 40 and 16 by 4, to get 10 - 4 = 6.


I hope this helps!

6 0
3 years ago
Read 2 more answers
Write in numeral form 4*100+2*10+8(6*1/10) +(1*1/100)
Mice21 [21]

Answer:428 7/100

Step-by-step explanation:

5 0
2 years ago
Pleaseeee answer as fast as possible
WINSTONCH [101]

Answer:

$986.84

Step-by-step explanation:

exchange rate is the rate at which one currency is exchanged for another currency

Amount of dollars bought = amount of RS / selling rate

75,000 / 76 = $986.84

5 0
2 years ago
Other questions:
  • Write two expressions where the solution is 41.
    5·1 answer
  • For this graph, mark the statements that are true.
    14·2 answers
  • 2x − 2) + (x + 1) + x + (x + 1) = (2x − 9) + (x + 1) + (x + 8) + x,
    8·2 answers
  • If the volume of the pyramid shown is 12 centimeters cubed, what is its height? A rectangular pyramid with a base of 3 centimete
    6·1 answer
  • PLEASE HURRY!!! AB = 20 cm, m∠A = 30° , and $m∠C = 45° . Express the number of centimeters in the length of BC in simplest radic
    11·1 answer
  • What is is the vertex of Y=(x-5)^2+8
    7·1 answer
  • Which of the following functions are continuous for all real numbers? \begin{aligned} &amp;h(x)= \log(x) \\\\ &amp;g(x)=\cot(x)
    10·1 answer
  • What is the sum (2/5 x + 5/8) + (1/5 x - 1/4)?
    8·1 answer
  • How would a bigger down payment be beneficial to borrowers? a. A bigger down payment is only beneficial for a person applying fo
    13·1 answer
  • Please Help I don’t get this!!!☹️☹️Im gonna have a meltdown!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!