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
What is a slope?and how do you find it on coordinate plain
Romashka-Z-Leto [24]
A slope is....
<span>a surface of which one end or side is at a higher level than another; a rising or falling surface.</span>

6 0
3 years ago
Read 2 more answers
Write a division equation that has a solution of 42
Allisa [31]
 Heres an equation: 126/3 = 42
4 0
3 years ago
Read 2 more answers
Four research teams each used a different method to collect data on how fast a new strain of maize sprouts. Assume that they all
Westkost [7]
<span>Confidence Level: 95%; Confidence Interval: 44 to 46</span>
5 0
3 years ago
Read 2 more answers
Use the following number line to determine if the expressions are true or false.
Usimov [2.4K]
True cus from point a and b is very low so true slime
6 0
3 years ago
One number is nine more than another number. If the sum of the number is 65, find both numbers
Aleonysh [2.5K]

Answer:

Step-by-step explanation:

x+x+9=65

2x=56

x=28

28,37

4 0
3 years ago
Read 2 more answers
Other questions:
  • In numerical expression [(25-11) (15-9)divided by 5
    10·1 answer
  • ?thx pls if U K Tell me the Answer thx
    7·2 answers
  • Ashley solved the equation for m using the following steps.
    8·2 answers
  • If 887 L = 108 B what is B if L is 25
    8·1 answer
  • Complete the two-column proof.
    8·2 answers
  • A construction worker drew a sketch he will use as he works. Which statement is not true? A. The distance from the ground to the
    11·2 answers
  • Which statement is true based on the information given on the coordinate plane select all that apply
    9·1 answer
  • What is 1 2/5 divided by 2 1/3
    12·1 answer
  • Please help, it would mean the world
    8·1 answer
  • 6th grade math i mark as brainliest​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!