Question

A large airport records the percentage of airline flights that land no later than 15 minutes after scheduled arrival. The average of these percentages for 12 months last year was 73.7​%. These data become available as soon as feasible.​ However, the airlines can provide preliminary results by obtaining a sample. The accompanying data contains the sample data indicating the number of minutes after scheduled arrival time that the aircraft arrived. Note that a negative entry indicates the minutes earlier than the scheduled arrival time that the aircraft arrived. Complete parts a through c below.

Arrival Time

3

-16

14

1

-18

-17

5

10

15

7

-15

7

20

-14

-4

8

-5

11

1

-13

17

5

4

5

3

9

2

15

-5

-10

-21

10

-14

50

6

-9

37

40

47

49

-14

-19

-19

-1

-21

55

-23

7

-14

3

28

-17

13

-1

4

-5

-2

40

5

11

55

3

7

-8

40

11

15

26

-18

-19

26

-20

5

7

15

42

-24

21

48

-14

-10

2

9

-5

-24

3

12

28

28

-14

9

11

-18

15

47

-18

-3

33

0

13

-15

15

-17

3

-5

23

8

4

-25

14

26

12

19

2

36

-15

1

12

19

27

-1

9

-7

23

-12

. Calculate the proportion of sampled airline flights that landed within 15 minutes of scheduled arrival.

_____________ ​(Round to three decimal places as​ needed.)

b. Calculate the probability that a sampled proportion of​ on-time flights would be within plus or minus0.05 of a population proportion equal to 0.737.

____________ ​(Round to four decimal places as​ needed.)

c. If the​ airlines' goal was to attain the same proportion of​ on-time arrivals as the previous​ year, do the preliminary results indicate that they have met this​ goal? Support your assertions.

A. The sample proportion is outside the interval found in part b. There is a large chance that a sample proportion would be outside this interval given the population proportion is still 0.737.

B. The sample proportion is contained in the interval found in part b. There is a large chance that a sample proportion would be contained in this interval given the population proportion is still 0.737.

C. The sample proportion is contained in the interval found in part b. There is a small chance that a sample proportion would be contained in this interval given the population proportion is still 0.737.

D. The sample proportion is outside the interval found in part b. There is a small chance that a sample proportion would be outside this interval given the population proportion is still 0.737.

Answer 1

a)

proportion of sampled airline flights that landed within 15 minutes of scheduled arrival=79/125 =0.632

b)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.737
sample size       =n=	125
std error of proportion=σp=√(p*(1-p)/n)=	0.0394

probability =

P(0.687<X<0.787)

=

P(-1.27<Z<1.27)=

0.8980-0.1020=

0.7960

c)

A. The sample proportion is outside the interval found in part b. There is a large chance that a sample proportion would be outside this interval given the population proportion is still 0.737.