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
dem82 [27]
2 years ago
11

You have received an order of 100 robotic resistance spot welders which contains 5 defective welders. You randomly select 15 wel

ders from the order without replacement to inspect to check whether they are defective.
(a) Determine the PMF of the number of defective welders in your sample? Remember to list all possible values of the random variable.
(b) Determine the probability that there are at least 4 defective welders in the sample? Hint: No need to calculate the final numerical results. Appropriately plugging in numbers in the mathematical expression is sufficient
Mathematics
1 answer:
erica [24]2 years ago
5 0

Answer:

a)

P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357

P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034

P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377

P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216

P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015

P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004

b) 0.154% probability that there are at least 4 defective welders in the sample

Step-by-step explanation:

The welders are chosen without replacement, so the hypergeometric distribution is used.

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

100 welders, so N = 100

Sample of 15, so n = 15

In total, 5 defective, so k = 5

(a) Determine the PMF of the number of defective welders in your sample?

There are 5 defective, so this is P(X = 0) to P(X = 5). Then

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357

P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034

P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377

P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216

P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015

P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004

(b) Determine the probability that there are at least 4 defective welders in the sample?

P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0015 + 0.00004 = 0.00154

0.154% probability that there are at least 4 defective welders in the sample

You might be interested in
Please help ASAP !!
timama [110]

Answer:

3rd one or infinite

Step-by-step explanation:

3 0
2 years ago
one batch of cookies makes 24 cookies. the recipe calls for 1 3/4 cups of flour. if Sarah needs to make 60 cookies how much flou
Svetllana [295]

Answer:

4 3/8 cups of flour needed for 60 cookies

Explanation:

You can multiply 24 by 2.5 to get 60 so you'd multiply the cups of flour by 2.5 as well. You multiply both of them by the same number because it's a ratio. You'd multiply then simplify to get the answer 4 3/8 cups of flour.

7 0
3 years ago
PLS ANSWER NOW
lora16 [44]
You're answers are a bit jumbled up but here is the answer:
T for Two
B for Blue
M for Moon Roof
F for four
G for Gray
NM for No Moon Roof... so

TBM
TBNM
TGM
TGNM
FBM
FBNM
FGM
FGNM
8 Possibilities



6 0
3 years ago
Read 2 more answers
What is the square footage of a 16in by 16in tile ​
sveta [45]

Answer:

the square footage is 256in

3 0
2 years ago
Which input in the table is incorrect?
Alex_Xolod [135]
Your answer should be b
6 0
3 years ago
Read 2 more answers
Other questions:
  • millie has a box of 1 hundresds cubes she also has a bag of 70 cubes how many trains of 10 cubes can she make
    5·1 answer
  • The number of people waiting in a line to buy tickets x minutes after a ticket booth open and is given by the expression 70-5x w
    9·2 answers
  • jon's car can travel an average of 35 miles per gallon. How many gallons will he need for a trip of 656 miles?
    14·1 answer
  • The quality control officer at a manufacturing plant needs to determine what percentage of items in a batch are defective. The f
    12·1 answer
  • Determine if each pair of ratios or rates are equivalent.
    7·1 answer
  • Deshaun exercises no less than 40 minutes per day.
    10·1 answer
  • Add at least 2 ways people in this job use arts and music ( that job is a dancer btw)
    15·1 answer
  • Please answer that for me i will mark brainliest<br> If X was 30, y would be equal to what number?
    5·1 answer
  • the ratios of the sides of a triangle are 3:2:4. if the shortest side is 26cm, what is the length of the longest side?
    12·1 answer
  • If you are choosing a single card from a standard deck of playing cards, what is
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!