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
sveticcg [70]
3 years ago
7

A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day of sharpness. If any dull blade

is found, the assembly is replace with a newly sharpened set of blades.
a. If 10 of the blades in an assembly are dull, what is the probability that the assembly is replaced the first day it is evaluated?

b. If 10 of the blades in an assembly are dull, what is the probability that the assembly is not replaced until the third day of evaluation? (Hint: assume that the daily decisions are independent and use the geometric distribution?

c. Suppose that on the first day of evaluation, 2 of the blades are dull. On the second day of evaluation 6 are dull; and on the third day of evaluation 10 are dull. What is the probability that the assembly is not replaced until the third day of evaluation? (Hint: assume that the daily decisions are independent. However the probability of replacement changes each day.
Mathematics
1 answer:
Alex73 [517]3 years ago
5 0

Answer:

Part a

The probability that assembly is replaced the first day is 0.7069.

Part b

The probability that assembly is replaced no replaced until the third day of evaluation is 0.0607.

Part c

The probability that the assembly is not replaced until the third day of evaluation is 0.2811.

Step-by-step explanation:

Hypergeometric Distribution: A random variable x that represents number of success of the n trails without replacement and M represents number of success of the N trails without replacement is termed as the hypergeometric distribution. Moreover, it consists of fixed number of trails and also the two possible outcomes for each trail.

It occurs when there is finite population and samples are taken without replacement.

The probability distribution of the hyper geometric is,

P(x,N,n,M)=\frac{(\limits^M_x)(\imits^{N-M}_{n-x})}{(\limits^N_n)}

Here x is the success in the sample of n trails, N represents the total population, n represents the random sample from the total population and M represents the success in the population.

Probability that at least one of the trail is succeed is,

P(x\geq1)=1-P(x

(a)

Compute the probability that the assembly is replaced the first day.

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly N = 48.

Number of blades selected at random from the assembly  n= 5

Number of blades in an assembly dull is M  = 10.

The probability mass function is,

P(X=x)=\frac{[\limits^M_x][\limits^{N-M}_{n-x}]}{[\limits^N_n]};x=0,1,2,...,n\\\\=\frac{[\limits^{10}_x][\limits^{48-10}_{5-x}]}{[\limits^{48}_5]}

The probability that assembly is replaced the first day means the probability that at least one blade is dull is,

P(x\geq 1)=1- P(x

(b)

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly  N = 48

Number of blades selected at random from the assembly  N = 5

Number of blades in an assembly dull is  M = 10

From the information,

The probability that assembly is replaced (P)  is 0.7069.

The probability that assembly is not replaced is (Q)  is,

q=1-p\\= 1-0.7069= 0.2931

The geometric probability mass function is,

P(X = x)= q^{x-1} p; x =1,2,....=(0.2931)^{x-1}(0.7069)

The probability that assembly is replaced no replaced until the third day of evaluation is,

P(X = 3)=(0.2931)^{3-1}(0.7069)\\=(0.2931)^2(0.7069)= 0.0607

(c)

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly   N = 48

Number of blades selected at random from the assembly  n = 5

Suppose that on the first day of the evaluation two of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M  = 2.

P(x=0)=\frac{(\limits^2_0)(\limits^{48-2}_{5-0})}{\limits^{48}_5}\\\\=\frac{(\limits^{46}_5)}{(\limits^{48}_5)}\\\\= 0.8005

Suppose that on the second day of the evaluation six of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M  = 6.

P(x=0)=\frac{(\limits^6_0)(\limits^{48-6}_{5-0})}{(\limits^{48}_5)}\\\\=\frac{(\limits^{42}_5}{(\limits^{48}_5)}\\\\= 0.4968

Suppose that on the third day of the evaluation ten of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M

= 10.

P(x\geq 1)=1- P(x

 

The probability that the assembly is not replaced until the third day of evaluation is,

P(The assembly is not replaced until the third day)=P(The assembly is not replaced first day) x P(The assembly is not replaced second day) x P(The assembly is replaced third day)

=(0.8005)(0.4968)(0.7069)= 0.2811

You might be interested in
Expand the function f(x)=(3x+2)
Usimov [2.4K]

Answer:

81x^4+216x^3+216x^2+96x+16

Step-by-step explanation:

6 0
2 years ago
Write the ratio as a fraction in simplest form a/b. What is the ratio of baseballs to basketballs?
Olin [163]
The ratio of baseballs to basketballs is

baseball: basketballs, or 

baseballs/basketballs

if you give me the numbers i can plug it in


hope this helps
7 0
3 years ago
What is Twice a number plus 4 is less then 12
sertanlavr [38]

Answer:

3

Step-by-step explanation:

3 x 2 = 6

6 + 4 = 10

10<12

Hope this helps!

3 0
3 years ago
Read 2 more answers
Which inequality does this graph represent?
sp2606 [1]

Yea the Answer is B: 3y - 6x > -6

I used Desmos (Graphing Calculator)

5 0
3 years ago
Read 2 more answers
What large grouping of elements do Halogens belong to? What are their distinct properties?
vekshin1
Group 17. They combine with alkali metals and form salt, the are reactive, they have 7 electrons in their outer energy level
5 0
3 years ago
Other questions:
  • If fg + gh = fh,which of the following statements must be true?
    7·1 answer
  • −4x+7y=3 solve for x and y
    11·1 answer
  • Solve y-12/25=3 1/5. What number is y?<br><br> A. 3 1/5<br> B. 3 17/25<br> C. 3 7/25<br> D. 4 17/25
    12·1 answer
  • A coin is tossed 4 times. What is the probability if getting 2 heads, 2 tails?
    13·2 answers
  • Help me please -no wrong answer = no Brainy, right answer = Brainiest
    14·1 answer
  • Multiply. 5 x 1 1/3<br> Answer with a mixed number in simplest form.
    5·2 answers
  • Ross is buying hats for his baseball team. Each package contains 4 hats. Generate the set of ordered pairs for the ratio relatio
    14·1 answer
  • 1- (-16) and 11- (11) just in case this information is needed it's integers I'm doing this for extra credit
    8·1 answer
  • I need help with this plz
    8·1 answer
  • A prize is divided in the ratio 5:1 if the larger share is £65 what is the total prize?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!