I\'ve been struggling with this one for a while. I need to write a 400 word summ

Question

I've been struggling with this one for a while. I need to write a 400 word summary afterward so if you could explain your reasoning that would be greatly appreciated!

1. Find the appropriate measure of center. 2. Find the appropriate measure of variation. 3. Select the appropriate probability distribution for a variety of data sets and estimating the parameters. 4. Calculate the probability that a flight will depart early or on-time. 5. Calculate the probability that a flight will arrive late. 6. Calculate the probability that a flight departs late or arrives early. 7. Find the graph(s) needed to appropriately describe the data.

DEP_DELAY ARR_DELAY -6 -40 -3 -9 -7 -30 -9 -31 26 30 -9 -25 3 8 11 6 -7 -26 -9 -16 -7 0 -12 -14 -4 -41 -5 30 -8 -6 -6 24 -5 -41 -8 24 -5 -32 -6 0 -2 -2 -3 10 6 -7 26 26 -2 -33 -1 7 15 -1 -10 -20 -2 -4 -7 -26 -8 -21 -8 -30 -1 -11 -6 6 -4 -41 -10 -22 -6 -19 58 49 44 60 -2 -34 -9 -14 -4 -2 3 -2 12 15 13 20 14 12 0 0 -6 -36 60 57 -9 7 35 36 9 22 -10 -25 -2 5 -7 15 -2 2 -1 -18 -3 23 9 1 -3 -8 -6 1 -6 -23 41 58 -6 -21 34 45 -10 6 18 1 -7 -19 -1 -22 -16 -18 0 -20 -4 -16 2 -6 6 7 16 14 -5 -13 85 65 50 40 -7 -27 -5 -26 -3 -16 43 48 -5 -2 -1 3 -3 -24 -10 0 -2 -4 -5 -14 8 -4 0 -27 -6 -4 -9 -21 196 182 -5 -55 -10 21 -2 -38 -4 -7 -2 6 -1 -27 -3 9 -7 -5 36 38 -6 -24 -4 -6 -2 -12 -4 -1 -10 -16 -3 -30 -8 9 -5 -28 94 76 -6 -10 -7 -8 -10 0 1 -14 -6 -48 -6 15 -2 -1 23 32 -11 -21 -3 -27 -6 -17 0 -31 5 7 -8 -20 -3 -1 17 19 6 2 -8 -13 -4 5 -2 -32 -5 -4 -5 -9 0 -10 -3 -7 -7 -24 5 -2 33 17 13 13 -4 -21 -6 5 -6 -27 -6 -15 14 23 3 13 -1 -3 9 -23 -3 18 -4 -22 0 -26 -6 -4 89 92 -9 -30 -9 -19 0 -6 -3 -9 -5 -6 24 7 8 11 -3 -21 7 -6 -2 -8 -2 -18 -1 -18 0 -6 2 1 -9 13 -2 -15 -3 1 4 -3 1 3 -6 20 -4 8 0 -23 0 -19 -8 -4 -6 -15 -2 -7 -5 2 -10 9 23 4 8 11 21 17 19 27 4 22 -4 6 15 0 22 24 25 29 -11 -3 -8 -17 1 0 -4 -1 -9 -7 -4 -11 -10 8 -11 -2 -8 -9 -6 -13 -11 -5 -4 -12 -16 -23 -3 -6 1 6 -4 -18 -4 -14 -6 -15 0 2 -8 -28 -4 -13 3 4 -4 -46 -4 -24 -8 -22 -7 -46 -5 -1 -2 -11 -5 -52 -9 -12 -1 -12 1 1 -5 -3 -6 1 -5 -25 -15 -23 13 -2 -7 -1 -9 -19 7 5 20 12 6 14 19 16 11 -3 57 42 -1 -17 -5 -2 -2 3 0 2 -9 -16 36 0 -8 -19 -2 -41 7 6 -10 -16 5 2 64 67 50 41 131 121 118 126 11 12 2 -2 -3 -1 -8 22 24 29 45 43 9 -20 0 -9 -8 7 -3 22 5 -2 3 -4 34 28 12 10 -3 -15 -1 -20 -6 -24 -11 11 17 14 -5 -6 -8 -5 -5 -12 -2 -13 28 7 -6 -18 -2 6 15 30 -5 -25 34 36 0 -7 -6 9 -10 -36 -5 -12 39 46 53 28 1 -4 -2 -13 -1 3 119 119 110 103 -2 7 -8 -2 -3 -2 -1 -12 10 9 4 -4 -10 -16 -3 -1 -4 -11 -9 -13 -1 -3 8 -4 -10 5 -6 9 36 35 6 13 -5 4 2 -9 -4 -11 -11 -31 -5 -10 -3 -17 24 19 -8 -1 -7 -17 -7 -19 -5 -13 -2 2 1 -2 -10 -7 -4 5 -9 -11 35 66 -4 2 -5 -9 0 2 -6 -11 -2 8 -6 -34 22 5 11 8 16 -2 -3 -7 -3 -6 -5 -11 -9 -13 -5 -10 -3 -3 -4 -6 28 21 2 -3 -2 -6 27 23 9 3 0 -12 3 18 0 4 -7 -7 -4 -4 -5 -11 -6 -26 -7 -14 -7 -14 9 -3 0 -2 -6 29 -5 -13 44 35 22 30 -2 -18 -3 -11 -7 -14 -8 -7 3 10 -4 6 0 14 -5 6 2 -7 -9 -22 -8 -16 3 5 26 23 -7 6 -1 0 -7 -8 -4 -19 -1 -21 -6 -1 -4 -2 72 69 -4 -7 -9 -11 17 -23 -10 7 -2 -5 -4 -10 -8 -21 1 -29 -11 -18 -4 -13 -4 2 -2 12 -2 6 3 4 -11 -28 -6 -11 -2 -27 -5 -19 -1 -1 -4 -10 -7 -22 -1 10 11 3 -5 3 -1 5 -9 -7 -6 -22 -8 -16 -8 -11 -6 -16 -13 -19 -4 -12 -6 -17 -4 4 -7 -20 -6 -31 2 -2 4 -6 -5 -13 -10 -9 44 38 -8 -18 -5 -4 -2 -2 -1 -12 17 -25 -3 -9 -5 -13 -3 -2 3 -26 -3 1 -11 -27 3 0 23 7 -5 -14 -5 -11 -6 1 -12 -17 45 31 -7 -22 -3 -11 -5 -10 -4 -16 -9 -13 -3 -11 -5 -13 -11 -14 27 19 11 7 -6 -19 -5 1 -3 -10 -5 -11 -3 -6 -3 28 28 18 12 -5 30 14 -6 -9 -6 -5 0 -5 -4 -6 -1 -10 -6 -17 12 27 15 20 3 12 19 17 48 46 -2 -8 -6 -2 -1 -29 -3 0 -6 9 3 -1 -12 -10 -9 -21 10 9 -3 3 -3 -7 -3 1 0 -9 3 -9 -12 -8 -1 -8 6 -4 72 77 -10 -16 -2 -3 -4 2 -4 11 20 20 -1 5 -12 -12 -2 -2 -9 -9 26 26 -3 -3 -5 -5 -6 -6 -17 -17

Explanation / Answer

1. Measure of centers can be mean or median in this case.

Mean for DEP_DELAY = 3.176

Median for DEP_DELAY = -3

Mean for ARR_DELAY = -1.5

Median for ARR_DELAY = -4.5

in this case we can chose Median as the appropriate measure of center since outliers are adding mean to be higher than median

2.Measure of variation:

Standard deviation can be considered the measure of deviation:

For DEP_DELAY std. deviation = 20.53

FOR ARR_DELAY std. deviation = 24.05

3. According to the given data, normal distribution with mean and standard deviation given above for dep_delay and arr_delay can be considered as probability distributions

4.The probability that flight will depart early on on time will be=

P(X<=0) = P((X-(-1.5))/24.05 <= 0.06) = 0.5249

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