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
Elden [556K]
3 years ago
13

United Airlines' flights from Denver to Seattle are on time 50 % of the time. Suppose 9 flights are randomly selected, and the n

umber on-time flights is recorded.
Mathematics
1 answer:
Ivanshal [37]3 years ago
6 0

Answer:

<u><em>a) The probability that exactly 4 flights are on time is equal to 0.0313</em></u>

<u><em></em></u>

<u><em>b) The probability that at most 3 flights are on time is equal to 0.0293</em></u>

<u><em></em></u>

<u><em>c) The probability that at least 8 flights are on time is equal to 0.00586</em></u>

Step-by-step explanation:

The question posted is incomplete. This is the complete question:

<em>United Airlines' flights from Denver to Seattle are on time 50 % of the time. Suppose 9 flights are randomly selected, and the number on-time flights is recorded. Round answers to 3 significant figures. </em>

<em>a) The probability that exactly 4 flights are on time is = </em>

<em>b) The probability that at most 3 flights are on time is = </em>

<em>c)The probability that at least 8 flights are on time is =</em>

<h2>Solution to the problem</h2>

<u><em>a) Probability that exactly 4 flights are on time</em></u>

Since there are two possible outcomes, being on time or not being on time, whose probabilities do not change, this is a binomial experiment.

The probability of success (being on time) is p = 0.5.

The probability of fail (note being on time) is q = 1 -p = 1 - 0.5 = 0.5.

You need to find the probability of exactly 4 success on 9 trials: X = 4, n = 9.

The general equation to find the probability of x success in n trials is:

           P(X=x)=_nC_x\cdot p^x\cdot (1-p)^{(n-x)}

Where _nC_x is the number of different combinations of x success in n trials.

            _nC_x=\frac{x!}{n!(n-x)!}

Hence,

            P(X=4)=_9C_4\cdot (0.5)^4\cdot (0.5)^{5}

                                _9C_4=\frac{4!}{9!(9-4)!}=126

            P(X=4)=126\cdot (0.5)^4\cdot (0.5)^{5}=0.03125

<em><u>b) Probability that at most 3 flights are on time</u></em>

The probability that at most 3 flights are on time is equal to the probabiity that exactly 0 or exactly 1 or exactly 2 or exactly 3 are on time:

         P(X\leq 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

P(X=0)=(0.5)^9=0.00195313 . . . (the probability that all are not on time)

P(X=1)=_9C_1(0.5)^1(0.5)^8=9(0.5)^1(0.5)^8=0.00390625

P(X=2)=_9C_2(0.5)^2(0.5)^7=36(0.5)^2(0.5)^7=0.0078125

P(X=3)= _9C_3(0.5)^3(0.5)^6=84(0.5)^3(0.5)^6=0.015625

P(X\leq 3)=0.00195313+0.00390625+0.0078125+0.015625=0.02929688\\\\  P(X\leq 3) \approx 0.0293

<em><u>c) Probability that at least 8 flights are on time </u></em>

That at least 8 flights are on time is the same that at most 1 is not on time.

That is, 1 or 0 flights are not on time.

Then, it is easier to change the successful event to not being on time, so I will change the name of the variable to Y.

          P(Y=0)=_0C_9(0.5)^0(0.5)^9=0.00195313\\ \\ P(Y=1)=_1C_9(0.5)^1(0.5)^8=0.0039065\\ \\ P(Y=0)+P(Y=1)=0.00585938\approx 0.00586

You might be interested in
A 55m and 35m broad park is surrounded by a 2.5m wide path.
daser333 [38]

Step-by-step explanation:

☄ \underline {\underline{ \text{Given}}} :

  • Length of a park ( l ) = 55 m
  • Breadth of a park ( b ) = 35 m
  • Width running outside the park ( d ) = 2.5 m
  • Rate of paving the path with stones = Rs 120 per sq.metre

☄ \underline{ \underline{ \text{To \: find}}}:

  • Area of the park
  • Cosy of paving the path with stones at Rs 130 per sq.metre

☄ \underline{ \underline{ \text{Solution}}} :

Part 1 : \boxed{\text{Area \:of \:a \:path \: running \:outside = 2d(l + b + 2d)}}

plug the known values and simplify :

⟹ \sf{2 \times 2.5(55 + 35 + 2 \times 2.5)}

⟹ \sf{5  \times 95}

⟹ \sf{475 \:  {m}^{2} }

Part 2 : \boxed{ \sf{Total \: cost = Area \: of \: paths \:  \times  Rate}}

⟹ \sf{475  \times 120}

⟹\sf{Rs \: 57000}

\purple{ \boxed{ \boxed{ \sf{ \tt{⟿ \: Our \: final \: answer : (i) = 475 \:  {m}^{2}   \:  and \: (ii ) = Rs \: 57000}}}}}

Hope I helped ! ♡

Have a wonderful day /night ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

7 0
3 years ago
Five friends Al, Bet, Cat, Don, and Ella live on the island where everyone is either a knight or a knave
nalin [4]

Answer:

?

Step-by-step explanation:

what am i tryign to solve here

8 0
3 years ago
Simplify 7 − 5(3)2 ?
Anastaziya [24]
The answer is 7 - 7.5

you multiply 5 and 3 and get 15 then divide by 2
8 0
2 years ago
Help? I'm not sure I understand how to solve this.
KiRa [710]
Okay so CBE is a right angle which equals 90 degrees. CBD and DBE makes up CBE which is 23 degrees is part of CBD. So subtract CBE from CBD to get DBE which is 67 degrees.
8 0
3 years ago
Solve for v.<br> Simplify your answer as much as possible.<br><br> 5+2v=3
Ksenya-84 [330]

Answer:

v= -1

Step-by-step explanation:

5+2v=3

2v=3-5

2v= -2

v= -2/2

v= -1

5 0
3 years ago
Read 2 more answers
Other questions:
  • Can somebody help me with these questions?
    5·1 answer
  • How do you long division
    11·1 answer
  • I need help please.
    13·1 answer
  • Find the average rate of change between f(-7) and f(-1) in the function f(x)=x^2+2x -8
    15·1 answer
  • How many hundreths are on 32.412?​
    15·2 answers
  • ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions
    9·1 answer
  • Which sentence fully illustrates that polygon ABCD is congruent to polygon PQRS?
    6·1 answer
  • D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2
    12·1 answer
  • Anna draws an angle in her notebook. In how many points do the rays intersect?
    14·1 answer
  • Hi please answer,
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!