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
Kitty [74]
3 years ago
14

A company that produces DVD drives has a 12% defective rate. Let X represent the number of defectives in a random sample of 55 o

f their drives.
Required:
a. What is the probability the sample will contain exactly 8 defective drives?
b. What is the probability the sample will contain more than 8 defective drives?
c. What is the probability the sample will contain less than 8 defective drives?
d. What is the expected number of defective drives in the sample?
Mathematics
1 answer:
EastWind [94]3 years ago
7 0

Answer:

a) 0.1287 = 12.87% probability the sample will contain exactly 8 defective drives

b) 0.2092 = 20.92% probability the sample will contain more than 8 defective drives.

c) 0.6621 = 66.21% probability the sample will contain less than 8 defective drives.

d) The expected number of defective drives in the sample is 6.6

Step-by-step explanation:

For each DVD, there are only two possible outcomes. Either it is defective, or it is not. The probability of a DVD being defective is independent of any other DVD, which means that the binomial probability distribution is used 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.

A company that produces DVD drives has a 12% defective rate.

This means that p = 0.12

Let X represent the number of defectives in a random sample of 55 of their drives.

This means that n = 55

a. What is the probability the sample will contain exactly 8 defective drives?

This is P(X = 8). So

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

P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287

0.1287 = 12.87% probability the sample will contain exactly 8 defective drives.

b. What is the probability the sample will contain more than 8 defective drives?

This is:

P(X > 8) = 1 - P(X \leq 8)

In which:

P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

Then

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

P(X = 0) = C_{55,0}.(0.12)^{0}.(0.88)^{55} = 0.0009

P(X = 1) = C_{55,1}.(0.12)^{1}.(0.88)^{54} = 0.0066

P(X = 2) = C_{55,2}.(0.12)^{2}.(0.88)^{53} = 0.0244

P(X = 3) = C_{55,3}.(0.12)^{3}.(0.88)^{52} = 0.0588

P(X = 4) = C_{55,4}.(0.12)^{4}.(0.88)^{51} = 0.1043

P(X = 5) = C_{55,5}.(0.12)^{5}.(0.88)^{50} = 0.1450

P(X = 6) = C_{55,8}.(0.12)^{6}.(0.88)^{49} = 0.1648

P(X = 7) = C_{55,7}.(0.12)^{7}.(0.88)^{48} = 0.1573

P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287

So

P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 + 0.1287 = 0.7908

P(X > 8) = 1 - P(X \leq 8) = 1 - 0.7908 = 0.2092

0.2092 = 20.92% probability the sample will contain more than 8 defective drives.

c. What is the probability the sample will contain less than 8 defective drives?

This is:

P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

With the values we found in b.

P(X < 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 = 0.6621

0.6621 = 66.21% probability the sample will contain less than 8 defective drives.

d. What is the expected number of defective drives in the sample?

The expected value of the binomial distribution is:

E(X) = np

In this question:

E(X) = 55(0.12) = 6.6

The expected number of defective drives in the sample is 6.6

You might be interested in
What fraction is equal to 0.25
Dmitry [639]

Answer:

Step-by-step explanation:

0.25 = 25/100=1/4

8 0
3 years ago
Read 2 more answers
12³.2².4⁴ / 4³.2.12²
Nuetrik [128]
Remember
\frac{xyz}{abc}=( \frac{x}{a} )( \frac{y}{b} )( \frac{z}{c} )
and
\frac{x^m}{x^n}=x^{m-n}

split them to have same bases
\frac{12^32^24^4}{4^32^112^2}=
( \frac{12^3}{12^2} )( \frac{4^4}{4^3} )( \frac{2^2}{2^1} )=
(12^1)(4^1)(2^1)=
(12)(4)(2)=
96
8 0
3 years ago
Read 2 more answers
Solve -14-5y &gt;-64<br> A. Y&lt;10<br> B.y&gt;-10<br> C. Y&gt;10<br> D.y&lt;-10
amm1812

Hello :D

Answer:

A. Y

Step-by-step explanation:

First, you add by 14 both sides of an equation.

-14-5y+14>-64+14

Then, simplify by equation.

-64+14=-50

-5y>-50

Multiply -1 both sides.

(-5y)(-1)<(-50)(-1)

5y<50

Divide by 5 both sides of an equation.

5y/5<50/5

Divide numbers from left to right.

50/5=10

y<10 is the correct answer.

Hope this helps you! :D

6 0
3 years ago
Oakville is a fungal disease that infects oak trees scientists have discovered that a single tree in a small forest is infected
Galina-37 [17]

Answer:

I solved part a

To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, getting that it will take 7.6 years for for 21 of the trees to become infected.

PART C

The logarithmic model is: g(x)= in x/0.4

We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.

Step-by-step explanation:

mark me brainliest!!

4 0
2 years ago
What is 70/10 equivalent fraction?
kaheart [24]
The answer is 7 because 70 ÷ 10 = 7.
6 0
3 years ago
Other questions:
  • Which phrase describes only a square?
    8·1 answer
  • What is the explicit rule for the sequence? 15.5, 13, 10.5, 8, 5.5, 3, ...  
    11·2 answers
  • What happens if you fail one semester in 8th grade?
    8·1 answer
  • Explain How you got that answer
    12·1 answer
  • The equation x^2+y^2-4x+2y=b describes a circle. Determine the y-coordinate of the center of the circle.
    14·2 answers
  • If someone please knows this please tell me
    15·1 answer
  • Solve the system of linear equations by substitution. 2x=y−10 x+7=y
    7·2 answers
  • Is the order of operations important why ?
    14·1 answer
  • Find the Ratio and the Exact value of the given Sin A.​
    7·1 answer
  • REARRANGE EQUATIONS PLEASE HELP ITS DUE IN TOMORROW
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!