Need help please tell me the answers for each one

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

pshichka [43]

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.

3 0

3 years ago

In standerd form what is the answer to y=6x-1 looking for x

horrorfan [7]

Answer:

x=1/6 or 1.16 (6 repeating) or x=6^-1

Step-by-step explanation:

y=6x-1

substitute y =0

0=6x-1

Move the variable to the left

-6x =-1

Divide on both dies

3 0

3 years ago

You put $100 in an account that<br> pays 5% interest yearly.

slavikrds [6]

Answer:

In a year, $105

In a decade, $150

In a century, $600

In a milleniun, $5100

Step-by-step explanation:

The formula is very simple: Multiply by 5 each year, and then you add it to the $100

8 0

3 years ago

Solve the rational equation: 7 - 2/x = 4 + 10/x

vlabodo [156]

Answer:

7 - 2 / x = 4 + 10 / x

or , 7 - 4 = 10 / x + 2 / x

or , 3 = 12 / x

or , x = 12 / 3

Therefore , x = 4

7 0

3 years ago

Read 2 more answers

Which team has the mode with the highest score?

Andrei [34K]

Team B has a mode of 60, which is the highest mode of all three teams. Team A has a mode of 48 and Team C has a mode of 30. Mode is the number that occurs most frequently in the set of data.

8 0

3 years ago