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
monitta
3 years ago
6

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight au

tomobiles, at least seven will have both headlights working?
Mathematics
2 answers:
lesya692 [45]3 years ago
8 0

Answer:

Required probability = 0.8131

Step-by-step explanation:

We are given that 90 percent of automobiles in Orange County have both headlights working.

Also, a sample of eight automobiles is taken.

Firstly, the binomial probability is given by;

P(X=r) =\binom{n}{r}p^{r}(1-p)^{n-r} for x = 0,1,2,3,....

where, n = number of trails(samples) taken = 8

           r = number of successes

           p = probability of success and success in our question is % of

                 automobiles in Orange County having both headlights working

                  i.e. 90%.

Let X = Number of automobiles in Orange County having both headlights working

So, X ~ Binom(n=8,p=0.9)

So, probability that in a sample of eight automobiles, at least seven will have both headlights working = P(X >= 7)

P(X >= 7) = P(X = 7) + P(X = 8)

                = \binom{8}{7}0.9^{7}(1-0.9)^{8-7} + \binom{8}{8}0.9^{8}(1-0.9)^{8-8}

                = 8*0.9^{7}*0.1 + 1*0.9^{8}  *1 = 0.3826 + 0.4305 = 0.8131 .

Marta_Voda [28]3 years ago
7 0

Answer:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:  

X \sim Binom(n=8, p=0.9)  

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

And for this case we want to find this probability:

P(X \geq 7) = P(X=7) +P(X=8)

And we can find the individual probabilities using the probability mass function

P(X=7)=(8C7)(0.9)^7 (1-0.9)^{8-7}=0.3826  

P(X=8)=(8C8)(0.9)^8 (1-0.9)^{8-8}=0.4305  

And replacing we got:

P(X \geq 7) = P(X=7) +P(X=8)=0.3826 +0.4305=0.8131

You might be interested in
X^2-5x=14 solve for x
elixir [45]

Answer:

x=7, -2.

Step-by-step explanation:

x^2-5x=14

x^2-5x-14=0

factor out the trinomial,

(x-7)(x+2)=0

zero property,

x-7=0, x+2=0,

x=0+7=7,

x=0-2=-2

8 0
3 years ago
Read 2 more answers
Please help ASAP is this correct?
emmasim [6.3K]

Answer:

yess that is correct

Step-by-step explanation:

18<27

7 0
3 years ago
Read 2 more answers
Nvm i got it lol sorry!
Dima020 [189]
Lol that’s good to hear I’m glad
4 0
2 years ago
The measure of an angle is 12° less than twice the measure of its supplement. What is the measure of the angle?
kupik [55]
Here is the equation you should use: x + 2x - 12 = 180    
You will be solving for x. 

Combine like terms then add twelve to both sides of the equation.

3x = 192

Divide by 3 on both sides of the equation. 

x = 64

Now, plug 64 in the equation for x. 

2(64) - 12 = 116
8 0
2 years ago
I need help on these three.
djyliett [7]

Step-by-step explanation:

I think it 1,180 yeah I think it is

7 0
3 years ago
Other questions:
  • A computer store has 75 printers of which 35 are laser printers and 40 are ink jet printers. if a group of 10 printers is chosen
    13·1 answer
  • Tickets to a musical cost $30 for adults and $12 for children. At one particular performance 960 people attended and $19 080 was
    7·2 answers
  • List possible rational zeros of f using the rational zero theorem. Then find all thezeros of the function.
    6·1 answer
  • Dan paid the grocery bill of $76.45 with $100. Mistakenly the cashier gave Dan only $13.55 in change. How much more does the cas
    8·2 answers
  • What is the measure of
    15·2 answers
  • Where is the point of concurrency of the angle bisectors of a triangle?
    5·1 answer
  • 3.3.31
    15·2 answers
  • Ginnys team scored 22 points during the first half of a basketball game.Her team scored 39 points during the second half of the
    13·2 answers
  • For the given corporate bond, whose annual simple interest rate is provided, find the
    7·2 answers
  • Find the perimeter of a 20 cm window
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!