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
Plz help me with this
Artemon [7]

Answer:

C Is the corect answer

Step-by-step explanation:

Brcause you multiple the 4 and 8 = 38

plus 3,000 = 7483 and you dicide 7483/2

= 250r + 250

6 0
2 years ago
Find the coordinates of the image of point R(4, –1) rotated 270 percent about the origin.
NeX [460]
(4,-1) turns into (1,4) because the equation for that is (x,y)->(y•-1,x)
8 0
2 years ago
Which of the following illustrates how to find the difference of 4h^5k and -7hk^5
MrRa [10]

Answer:

Not possible

Step-by-step explanation:

Which of the following illustrates how to find the difference of 4h^5k and -7hk^5

Takig the difference

4h^5k - (-7hk^5)

= 4h^5k +7hk^5

Collect the like terms

= hk(4h^4+7k^5)

Hence the difference is not possible

7 0
3 years ago
A rectangle has vertices at these coordinates.
kompoz [17]
(6,2) is the fourth vertex
8 0
3 years ago
Read 2 more answers
A vehicle 1 1/8 uses gallons of gasoline to travel 13 1/2 miles. At this rate, how many miles can the vehicle travel per gallon
alexgriva [62]

Answer: 12 miles per gallon

trust

me

on

my

mama

this

is

correct

my

g

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the greatest common factor of 9x^{2}y9x 2 y and 5x^{4}y^{2}5x 4 y 2 ?
    8·1 answer
  • In a pack of 52 cards, 4 of the cards are kings. the first card is picked, the results are recorded and the card is returned to
    10·1 answer
  • 145 pounds to 132 pounds
    15·2 answers
  • The sale price of an item is $180 after a 25% discount is applied. What is the original price of the item?
    10·2 answers
  • An amateur radio operator erects a 75-foot vertical tower for an antenna. A 117 guy wire is pulled from the top of the tower dia
    6·1 answer
  • The sum of 6 and another number is 23, write and solve an equation to find the other number
    8·2 answers
  • Un numero mas su doble es igual a su mitad mas quince ¿cual es el numero ?
    9·1 answer
  • Show that (x+5)^2-(x-5)^2=20x
    15·1 answer
  • Help me please I’m not so smart hehe
    15·1 answer
  • Dean's father, Franco, is 5 times his age. Dean is 8 years older than his sister, Helen. The sum of their ages is 62 years. How
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!