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
nirvana33 [79]
3 years ago
14

A company that produces fine crystal knows from experience that 13% of its goblets have cosmetic flaws and must be classified as

"seconds." (Round your answers to four decimal places.)
(a)Among six randomly selected goblets, how likely is it that only one is a second?
(b)Among six randomly selected goblets, what is the probability that at least two are seconds?
(c)If goblets are examined one by one, what is the probability that at most five must be selected to find four that are not seconds?
Mathematics
1 answer:
Kisachek [45]3 years ago
8 0

Answer:

(a) The probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b) The probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c) The probability that at most five must be selected to find four that are not seconds is 0.9453.

Step-by-step explanation:

Let <em>X</em> = number of seconds in the batch.

The probability of the random variable <em>X</em> is, <em>p</em> = 0.31.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.

The probability mass function of <em>X</em> is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...

(a)

Compute the probability that only one goblet is a second among six randomly selected goblets as follows:

P(X=1)={6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=6\times 0.13\times 0.4984\\=0.3888

Thus, the probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b)

Compute the probability that at least two goblet is a second among six randomly selected goblets as follows:

P (X ≥ 2) = 1 - P (X < 2)

              =1-{6\choose 0}0.13^{0}(1-0.13)^{6-0}-{6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=1-0.4336+0.3888\\=0.1776

Thus, the probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c)

If goblets are examined one by one then to find four that are not seconds we need to select either 4 goblets that are not seconds or 5 goblets including only 1 second.

P (4 not seconds) = P (X = 0; n = 4) + P (X = 1; n = 5)

                            ={4\choose 0}0.13^{0}(1-0.13)^{4-0}+{5\choose 1}0.13^{1}(1-0.13)^{5-1}\\=0.5729+0.3724\\=0.9453

Thus, the probability that at most five must be selected to find four that are not seconds is 0.9453.

You might be interested in
I've been stuck on this for about 2 hours but it still doesn't make any sense to me, please helpppppppppp
Mariana [72]
I really hope this helps. I’m sure the answer is c:)
5 0
3 years ago
what the area of a triangle whose base is 23 inches and whose height is 28. write your answer in decimal
Aneli [31]

Answer:

322

Step-by-step explanation:

Triangle area = base*height)2Here, area = 23*28/2=322

5 0
2 years ago
Read 2 more answers
Evaluate the following equation for p:<br> -3p + 6 + 7p = 22
strojnjashka [21]

Answer:

4

Step-by-step explanation:

-3p+6+7p=22

-3p+7p=16

4p=16

p=4

5 0
2 years ago
Read 2 more answers
Pls help first one gets brainliest (must show work)
worty [1.4K]

Answer:

I got this. Use the order PEMDAS search Up if you don’t know what it means.

Step-by-step explanation:

Start with What’s inside the parentheses

(X - 3) = 3x

(X + 5) = 5x

The divide.

How to divide it - The number coefficients are reduced the same as in simple fractions. When dividing variables, you write the problem as a fraction. Then, using the greatest common factor, you divide the numbers and reduce. You use the rules of exponents to divide variables that are the same — so you subtract the powers.

3 0
3 years ago
Read 2 more answers
Whitch is the value of this expression when a=5 and k=-2
lana66690 [7]

Answer:

25/9

Step-by-step explanation:

25/9

7 0
3 years ago
Other questions:
  • The base of the figure shown is a cube with sides that are 12 inches long. The total height of the figure is 20 inches. The slan
    9·2 answers
  • A line has a rise of 6 and a slope of 1/20. What is the run?
    8·2 answers
  • Find the domain for the rational function f(x)=x-1/x+3
    15·1 answer
  • What are the vertical asymptotes of f(x)=10/x^2-1
    8·1 answer
  • Graph g(x)= 1/3x^2 and f(x) =x^2
    14·1 answer
  • -11 &lt;2k +9 313<br> I need help
    9·1 answer
  • A plane flew between two cities at 330 mi/hr; a car went the same distance at 55 mi/hr. If the car took 7.5 hr longer, how far a
    13·1 answer
  • Do you know this please
    14·1 answer
  • HEEEEEEEEELP!!!!!!!!!!!!!!!!!!!!!!!!!!
    13·1 answer
  • True or False? (2,-2) is the solution to the system of equations.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!