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expeople1 [14]
3 years ago
5

A small regional carrier accepted 23 reservations for a particular flight with 20 seats. 14 reservations went to regular custome

rs who will arrive for the flight. each of the remaining passengers will arrive for the flight with a 50 % chance ,independently of each other.
Find the probability that overbooking occurs

find the probability that the flight has empty seats​
Mathematics
1 answer:
MrRissso [65]3 years ago
7 0

Answer:

- The probability that overbooking occurs means that all 8 non-regular customers arrived for the flight. Each of them has a 56% probability of arriving and they arrive independently so we get that  

P(8 arrive) = (0.56)^8 = 0.00967

- Let's do part c before part b. For this, we want an exact booking, which means that exactly 7 of the 8 non-regular customers arrive for the flight. Suppose we align these 8 people in a row. Take the scenario that the 1st person didn't arrive and the remaining 7 did. That odds of that happening would be (1-.56)*(.56)^7.

Now take the scenario that the second person didn't arrive and the remaining 7 did. The odds would be  

(0.56)(1-0.56)(0.56)^6 = (1-.56)*(.56)^7. You can run through every scenario that way and see that each time the odds are the same. There are a total of 8 different scenarios since we can choose 1 person (the non-arriver) from 8 people in eight different ways (combination).  

So the overall probability of an exact booking would be [(1-.56)*(.56)^7] * 8 = 0.06079

- The probability that the flight has one or more empty seats is the same as the probability that the flight is NOT exactly booked NOR is it overbooked. Formally,  

P(at least 1 empty seat) = 1 - P(-1 or 0 empty seats)  

= 1 - P(overbooked) - P(exactly booked)

= 1 - 0.00967 - 0.06079  

= 0.9295.

Note that, the chance of being both overbooked and exactly booked is zero, so we don't have to worry about that.

Hope that helps!

Have a great day :P

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yan [13]

Answer:

8 ,d=4       9, -3e/2=-24  10, all real numbers  11, p=9/2 12, x=10 13, No Solution

Step-by-step explanation:

If any of these are incorrect I apologize but you are in college and you did not mention if you took calculus trigonometry or Statistics if they are wrong tell me what class it is you take and I will gladly fix them for you :D

4 0
3 years ago
Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to hav
Svetllana [295]

Answer:

She needs a sample of at least 385.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

How large a sample should she take to achieve this?

She needs a sample of size at least n.

n is found when M = 0.04.

We do not know the true population proportion, so we use \pi = 0.5, which is the case for which we are going to need the largest sample size.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.05\sqrt{n} = 1.96*0.5

Dividing both sides by 0.05

\sqrt{n} = 19.6

(\sqrt{n})^{2} = 19.6^{2}

n = 384.2

Rounding up

She needs a sample of at least 385.

3 0
3 years ago
Convert n √a into pure surds​
Brrunno [24]

Answer:

√n²a

Step-by-step explanation:

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4 0
2 years ago
ADHE - ADGF below. Find the value of 'x'.<br> X<br> H н<br> E<br> 8<br> 2.<br> 12
Vlad1618 [11]

Given:

\Delta DHE\sim \Delta DGF

To find:

The value of x.

Solution:

We know that, corresponding sides of similar triangles are proportional.

Since,\Delta DHE\sim \Delta DGF, therefore

\dfrac{HE}{GF}=\dfrac{DE}{DF}

On substituting the values from the figure, we get

\dfrac{8}{12}=\dfrac{x}{x+2}

\dfrac{2}{3}=\dfrac{x}{x+2}

On cross multiplication, we get

2(x+2)=3x

2x+4=3x

4=3x-2x

4=x

Therefore, the value of x is 4.

8 0
2 years ago
a farmer has one square mile of land if he divides his land into square fields that are half mile long and half my wife how many
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