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
dmitriy555 [2]
3 years ago
12

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the

contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected.
(A) Based on this sampling plan, the probability that a batch that meets the contract requirements will be shipped without further inspection is approximately___________.
Mathematics
2 answers:
zalisa [80]3 years ago
7 0

Answer:

The answer is 0.9138

Step-by-step explanation:

This is a question of Binomial Probability Combination and the formula that will be used in this question is:

P(x) = nCx * p^{x} * q^{n - x}

Where,

  • n ⇒ Finite sample number, here it is equal to 10
  • p ⇒ Success, here it is equal to 5% defective or \frac{5}{100} = 0.05
  • q ⇒ Failure, here it is equal to (1 - p) i.e. q = 1 - \frac{5}{100} = 0.95
  • x ⇒ Number of defective products

Now, in order to to pass inspection and be shipped x needs to be equal to '0' or '1'.

So,

Putting x = 0 in the formula along with the values mentioned above we get

P(0) = 10C0 * 0.05^{0} * 0.95^{10 - 0}

P(0) = 1 * 1 * 0.5987

P(0) = 0.5987

Similarly,

Putting x = 1 in the formula along with the values mentioned in the bullets above we get

P(1) = 10C1 * 0.05^{1} * 0.95^{10 - 1}

P(1) = 10 * 0.05 * 0.6302

P(1) = 0.3151

Now, in order to get the actual probability we need to add P(0) and P(1) because there is a chance that either there is no defective product or there is 1 defective in the shipped-batch from which sample was taken. Hence,

P(0) + P(1) = 0.5987 + 0.3151

= 0.9138 (Answer)

agasfer [191]3 years ago
4 0

Answer:

0.9138 = 91.38%

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of other items. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which 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)!}

And p is the probability of X happening.

10 items

This means that n = 10

5 percent of the items shipped can be defective.

This means that p = 0.05

Probability that a batch that meets the contract requirements will be shipped without further inspection

Probability of 1 or fewer defects.

So

P(X \leq 1) = P(X = 0) + P(X = 1)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.05)^{0}.(0.95)^{10} = 0.5987

P(X = 1) = C_{10,1}.(0.05)^{1}.(0.95)^{9} = 0.3151

P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5987 + 0.3151 = 0.9138

So the answer is:

0.9138 = 91.38%

You might be interested in
If m = 22 and n = 3, what is the value of the following expression? m - 5 • n + 3 A. 51 B. 10 C. 4 D. 54
melisa1 [442]

The answer is B, 10.


Step-by-step explanation: You plug in the values where the variables are, then follow PEMDAS, beginning with 5 times 3.


4 0
3 years ago
Make x the subject of the formula<br> p+x=t
yan [13]

Answer:

x=t-p

Step-by-step explanation:

just move p to the other side and since it crosses the equals sign so you have to change it from positive to negative

4 0
3 years ago
Read 2 more answers
Use the intersect method to solve the equation x^2-1=-x^2+7
olga55 [171]

Answer:

The solutions of the equation x^2-1=-x^2+7 are (-2,3) and (2,3)

Step-by-step explanation:

Please, see the attached file.

Thanks.

4 0
3 years ago
HURRY!!!!!
belka [17]

Answer:

y=10

Step-by-step explanation:

what ever x='s you add 5 and what ever y='s you subtract 5

4 0
3 years ago
Read 2 more answers
A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find
zysi [14]

Answer:

( t - p ) /  85x =  h

( t - 265.95 ) /  85x  = h

648.45 - 265.95 / 85x = 3.32h

h = 3.32

Therefore ( t - p ) /  85x =  3.32

Step-by-step explanation:

648.45 - 265.95

282.50 /85

= 3.32 hrs

Finding equation to find hours can be shown as

( t - p ) /  85x =  3.32

How we found equation to find total

Parts = 19 x 14 - 5/100 = 266- 0.05

648.45 - 265.95 = 282.5

282.5/85 = 3.323  near to 3,233529

Labour = 85x  = 17 (5 + x)

Equation = 17(5+ x) + 14(19) - 5/100 = 648.45 where x = 85

Equation = ( 85x x 3  1/3) + 265 - 19/20 = t

3 0
2 years ago
Other questions:
  • How do you write 74171.7 in scientific notation
    9·2 answers
  • Probablity of getting a number greater than 4 when a die is rolled one time
    6·2 answers
  • Write an expression that shows how to multiply 7 x 256 using expanded form and the distributive property
    10·2 answers
  • Please help!! Choose the equation below that represents the line passing through the point (−5, 1) with a slope of 3/2
    14·1 answer
  • A cylinder has a radius of 12m and a height of 30m. Find the surface area and volume
    12·1 answer
  • Given the points (3, -1) and (-8, 0) find the slope.
    15·1 answer
  • Sam is climbing 2/3 m every 15 minutes.<br> How many meters will he climb in 1<br> hour?
    8·2 answers
  • Help please no links!! Step by step
    13·1 answer
  • An oil tanker is leaking at a constant rate per minute. After 11 minutes, 931 gallons of oil remain in the tanker. After 18 minu
    13·1 answer
  • HELP Solve for x and y
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!