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
sweet [91]
3 years ago
6

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, So

uthwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 10 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 3 flights arrive late.
Mathematics
1 answer:
pshichka [43]3 years ago
3 0

Answer:

There is a 32.22% probability that at least 3 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives on time, or it arrives late. This means that we can solve this problem using binomial probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

In this problem, we have that:

There are 10 flights, so n = 10.

A success in this case is a flight being late.  80% of its flights arriving on time, so 100%-80% = 20% arrive late. This means that \pi = 0.2.

(a) Find the probability that at least 3 flights arrive late.

Either less than 3 flights arrive late, or at least 3 arrive late. The sum of these probabilities is decimal 1. This means that:

P(X < 3) + P(X \geq 3) = 1

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684

P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020

So

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778

Finally

P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222

There is a 32.22% probability that at least 3 flights arrive late.

You might be interested in
jerry needs 2 gallons of paint to 600 square feet of wall space. how much area could he cover with 5 gallons of paint
klemol [59]

Answer:

1500 square feet

Step-by-step explanation:

2 gallons of paint can cover 600 square feet

the ratio is 2:600 if you simplify you will get 1:300

We need to find how much we can cover with 5 gallons so just times each side of the ratio by 5 after simplifying.

Hope this helps

4 0
3 years ago
When traveling with the wind, it takes an airplane 3 hours to travel 1800 miles. It takes the same airplane 3.6 hours to travel
Alla [95]

Answer:

2000

Step-by-step explanation:

6 0
2 years ago
If we solve an equation for a variable x what should our final equation look like ?
Nesterboy [21]
You can solve an easy equation in your head by using the multiplication table.
6 0
3 years ago
Can you please help me with this?
love history [14]

Answer:

36 cm squared is the anwer

5 0
3 years ago
Read 2 more answers
How are ∠1 and ∠2 related
andreyandreev [35.5K]

Answer:

  • D. They are adjacent

Step-by-step explanation:

Angles 1 and 2 have common side, so they are adjacent. They are not making a right or straight angle.

Correct choice is D

7 0
2 years ago
Other questions:
  • 3 – 3x = 3(1 – x)<br> Is is commutative property identity property or distributive property
    7·1 answer
  • A drama club is selling tickets to the spring musical. The auditorium holds 200 people. Tickets cost $12 at the door and $8.50 i
    10·1 answer
  • Bank tellers earn a weekly
    5·1 answer
  • each game cost 39.99 and there is a 4.85 shipping charge per order how much will it cost him to order any number of video games
    10·1 answer
  • At the Shake Shack two orders of fries
    13·1 answer
  • Can someone help me with question 19 and 21 please?
    14·1 answer
  • A square playground has an area of 279 ft. ² What is the approximate length of each side of the playground?
    7·1 answer
  • Find the surface area of the figure below:​
    14·2 answers
  • Consider the graph of f(x)=13x−2. How do the graphs of 2f(x), f(x+2), and f(x)+2 compare to the graph of f(x)? Drag tiles to the
    12·1 answer
  • 7,500 to 8,200
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!