Question

Dep Delay Arr Delay q1 -13 -9 q3 1 3 IQR 14 12 stdev 9.211846 9.660933...

Dep Delay Arr Delay
q1 -13 -9
q3 1 3
IQR 14 12
stdev 9.211846 9.660933
negative 291
zero 39
positive 170
total (should be 500) 500

all data is for arrival data. please help me explain these

can someone help me answer these questions and tell me how to put them in excel.thanx in advance

1.    Define a random variable (X) so that your chosen data set represents values of X.

2.    Is your chosen random variable discrete or continuous? Explain how you know

3. Would the Normal or Binomial distribution be a good fit for the underlying sample distribution of X? If one of them is a good fit, state how you would approximate the distribution parameters.

4.    Calculate the probability that a flight will depart early or on time.

(8). Calculate the probability that a flight will arrive late.

6. Calculate the probability that a flight departs late or arrives early.

7. Assume now that the random variable X=Arrival Time is exactly normally distributed with mean m= -2.5 and standard deviation s= 23. Compute the probability of a flight arriving late based on this new information. Does this contradict your answer from Part 8?

Your Histogram

Mean

-3.138

Standard Deviation (s)

9.66093

Lowest Score

-29

Highest Score

26

Distribution Range

55

Total Number of Scores

500

Number of Distinct Scores

53

Lowest Class Value

-30

Highest Class Value

32

Number of Classes

7

Class Range

9

data set

ARR_Delay
0
-3
-5
-1
3
-5
8
6
0
-12
0
-2
-10
12
-13
4
-1
2
-14
0
-23
10
-20
26
-25
7
-3
0
0
-2
-3
-6
-9
6
-7
-4
-9
4
12
0
-4
-17
-18
15
20
12
0
-14
5
7
8
22
-5
1
0
2
-3
7
1
-2
1
-1
6
-7
0
6
1
-17
-16
-2
-1
-6
-17
7
14
-13
11
12
-2
-4
0
3
-4
3
0
0
-6
-8
-8
-12
-10
-9
6
-13
3
0
-13
6
-17
9
-19
13
-2
-21
-16
-28
-14
-2
4
-2
6
-6
-1
0
-8
0
2
-13
2
-11
-7
-1
-7
7
-1
-21
19
2
-12
5
-22
-24
-20
-20
-1
-1
-4
3
5
-6
5
-6
-9
10
13
-12
-9
1
-14
-12
-16
8
-14
-4
-18
-16
-20
7
11
-8
-24
0
-2
0
-1
1
4
-5
1
-9
3
6
8
-9
-15
-14
-4
-13
2
9
4
11
17
1
22
6
0
24
1
-2
-1
0
-7
-2
-9
8
-10
-4
-1
-10
-4
-11
-12
6
-2
-7
-7
2
-20
-12
4
-8
-4
-7
-14
-3
-4
-2
-2
-4
1
-7
1
-11
-3
-12
-14
-13
5
12
14
16
-18
20
-6
-22
3
2
-11
0
-10
-19
2
-4
2
4
1
4
6
1
-10
-12
8
14
11
-14
-9
7
2
-19
-18
5
10
-10
-6
-3
11
14
-24
-3
-3
-5
0
-6
6
0
-8
0
-6
9
-9
-4
12
10
-15
-7
3
9
11
7
-23
-24
-15
9
-25
-14
-3
-4
-5
-4
-4
5
9
2
1
4
-5
-4
-1
-7
-1
0
-19
-4
-3
-10
2
-23
-19
5
-17
8
2
-3
2
-1
1
-6
5
8
-9
-5
-7
-3
-2
-6
-14
-12
2
-17
-15
1
3
-12
18
4
-20
-24
-18
-4
-2
-1
-3
-5
5
-5
5
8
-6
-2
0
-8
10
6
14
6
-13
-20
-6
5
23
6
0
-19
-9
-8
-29
-2
4
-5
-3
-1
7
-5
-1
-3
-10
-10
-2
2
12
6
4
-12
-10
-17
-4
-23
-15
-4
10
3
3
5
-1
-3
-2
-3
0
-8
-8
-5
4
-6
-11
-13
-10
-4
-9
0
-2
-17
-20
-11
-23
-16
-13
-25
-2
1
-3
0
2
-4
-3
1
-1
1
0
-1
-3
-12
-2
-5
-4
-4
0
7
-2
1
-13
-13
-19
2
18
-23
14
-21
-3
0
0
-4
-7
0
0
1
5
7
-6
-13
-3
0
9
-18
0
0
9
3
-17
1
-17
-18
-20
-21
-26
1
-4
-3
2
3
2
5
-5
-9
-4
13
-3
-5
-3
-1

All calculations must be performed in Excel. The Excel file must be submitted as part of the report. Preferred method is pasting your Excel calculations into this paper instead of including a separate file.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

1.    Define a random variable (X) so that your chosen data set represents values of X.

Here X is the Arrival Time of the flight

2.    Is your chosen random variable discrete or continuous? Explain how you know

Here the random variable is continous. Here the value is continous because it takes any value, not some specific value so that shows continuity.

3. Would the Normal or Binomial distribution be a good fit for the underlying sample distribution of X? If one of them is a good fit, state how you would approximate the distribution parameters.

Here the normal distirbution would be a better fit because binomial distribution is a discrete one.

Here the distribution parameters are

mean = -3.138 min

standard deviation = 9.661 min

4.    Calculate the probability that a flight will depart early or on time.

Here we have to put the data array in excel and calculate the number of values that are less than or equal to zero.

P(On time) = (291 + 39)/500 = 330/500 = 0.66

(8). Calculate the probability that a flight will arrive late.

P(Late flight) = 170/500 = 0.34

6. Calculate the probability that a flight departs late or arrives early.

Pr(flight departs late of arrives early) = 1 - Pr(Not coming on time) = 1 - 39/500 = 0.922

7. Assume now that the random variable X=Arrival Time is exactly normally distributed with mean m= -2.5 and standard deviation s= 23. Compute the probability of a flight arriving late based on this new information. Does this contradict your answer from Part 8?

Here now we use Excel here

Put the formula

P(aarival late) = 1 - Pr(x < 0 ; -2.5; 23) = 1 - NORMDIST(0, -2.5, 23, true) = 1- 0.5433 = 0.4567

yes this probability is much higher than the probability we observe.

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