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
PLEASE HELP ME
monitta

Answer:

b

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Classify the triangle by its sides, and by its angles ​
ivolga24 [154]
There is no triangle
5 0
2 years ago
There are 4 red marbles and 8 green marbles in a box. If Emma randomly selects a marble from the box, what is the probability of
murzikaleks [220]

Answer:

The probability of a successful event is the ratio of the number of successful events to the total number of events. In this case, a successful event is selecting a red marble from the box. The total number of events is the total number of marbles in the box:

Red marbles/Total number of marbles

4/12 divide

=1/3

3 0
3 years ago
What is an equation of the line that passes through the point ( 6 , − 1 ) (6,−1) and is parallel to the line x − 3 y = 3 x−3y=3?
Nataly [62]

Answer:

y = 1

Step-by-step explanation:

Passes through (6,-1)(6,-1)

Find the slope (m)

m=(y2 - y1) / (x2 - x1)

m=(-1 - (-1) ) / (6-6)

m= 0

Parallel to x - 3y = 3

-3y = -x +3

y = 1/3 x -1

Equation of the line equation is y - y1 = m ( x - x1 )

y - ( -1 ) = 0 ( x - 6 )

y + 1 = 0

y = 1

4 0
3 years ago
Find the volume of the prism
leva [86]

Using the formula given for area:

Area = 1/2 (7 +5)4 = 1/2(12)4 = 24 square cm.

Now to find the volume multiply the area by the depth:

24 x 6 = 144 cubic cm.

8 0
2 years ago
Other questions:
  • Geometry help?<br> 24/10<br> 10/24<br> 24/26<br> 10/26
    9·1 answer
  • Type in expanded form. Use to indicate multiplication. 5^2
    9·1 answer
  • A boat travels 350.7 miles in 35.1 hours with a constant speed how far can you travel 19. Six hours with the same speed
    8·1 answer
  • Evaluate the expression of 8x - 20 if x=10
    12·1 answer
  • What is the answer (9+43-2)2-10-5 to the 2nd power
    10·1 answer
  • PLZZZ HELP ME!<br> help me
    8·1 answer
  • Given the equation below, if x = 4, what is the value of y? y=14x
    6·1 answer
  • Is the equation y=3x + 10 proportional? Explain how you know
    8·2 answers
  • What is 12.4% of 250 :Step by step explanation Please​
    5·1 answer
  • Michael makes 60% of his free-throw attempts. If Michael attempts two free-throws,
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!