Question

question 9 of 10
the following set of random numbers represents 20 simulations of three
daily flights from philadelphia to seattle, with 0, 1, 2, or 3 representing a late
departure and 4, 5, 6, 7, 8, or 9 representing an on-time departure. in how
many of the simulations was there an on-time departure for all three flights?
506 619 535 769 096 380 527 555 737 192 092 658 694 320 442 812 968
765 374 282

a. 4
b. 5
c. 3
d. 6

Explanation:

Step1: Understand the criteria

On - time departure is represented by 4, 5, 6, 7, 8, 9. We need to check each 3 - digit number (simulation) to see if all three digits are in {4,5,6,7,8,9}.

Step2: Check each simulation

• 506: 0 is not on - time (reject)
• 619: 1 is not on - time (reject)
• 535: 3 is not on - time (reject)
• 769: 7,6,9 are on - time (accept)
• 096: 0 is not on - time (reject)
• 380: 3,0 are not on - time (reject)
• 527: 2 is not on - time (reject)
• 555: 5,5,5 are on - time (accept)
• 737: 3 is not on - time (reject)
• 192: 1,2 are not on - time (reject)
• 092: 0,2 are not on - time (reject)
• 658: 6,5,8 are on - time (accept)
• 694: 6,9,4 are on - time (accept)
• 320: 3,2,0 are not on - time (reject)
• 442: 2 is not on - time (reject)
• 812: 1,2 are not on - time (reject)
• 968: 9,6,8 are on - time (accept)
• 765: 7,6,5 are on - time (accept)
• 374: 3 is not on - time (reject)
• 282: 2,2 are not on - time (reject)

Now count the accepted ones: 769, 555, 658, 694, 968, 765. Wait, wait, let's recount:

Wait 769 (1), 555 (2), 658 (3), 694 (4), 968 (5), 765 (6)? Wait no, maybe I made a mistake. Wait the original list: let's list all 20 simulations:

1. 506
2. 619
3. 535
4. 769
5. 096
6. 380
7. 527
8. 555
9. 737
10. 192
11. 092
12. 658
13. 694
14. 320
15. 442
16. 812
17. 968
18. 765
19. 374
20. 282

Now re - check:

• 769 (digits 7,6,9: all on - time) - 1
• 555 (5,5,5: all on - time) - 2
• 658 (6,5,8: all on - time) - 3
• 694 (6,9,4: all on - time) - 4
• 968 (9,6,8: all on - time) - 5
• 765 (7,6,5: all on - time) - 6? Wait no, the options are 4,5,3,6. Wait maybe I misread the list. Let's check the original numbers again:

The list is: 506 619 535 769 096 380 527 555 737 192 092 658 694 320 442 812 968 765 374 282. Wait that's 19 numbers? Wait the problem says 20 simulations. Maybe a typo, but let's check again.

Wait 769 (1), 555 (2), 658 (3), 694 (4), 968 (5), 765 (6). But the options have 6 as D. Wait maybe my initial check was wrong. Wait 442: 4,4,2. 2 is not on - time. 812:8,1,2. 1,2 not. 374:3,7,4. 3 not. 282:2,8,2. 2s not. 765:7,6,5 (all on - time). 968:9,6,8 (all). 694:6,9,4 (all). 658:6,5,8 (all). 555:5,5,5 (all). 769:7,6,9 (all). So that's 6? But the options have D as 6. Wait maybe I miscounted earlier. Let's check each of the 20 (wait the list given: 506,619,535,769,096,380,527,555,737,192,092,658,694,320,442,812,968,765,374,282. That's 19? Maybe a typo, but according to the options, D is 6. Wait maybe my first check was wrong. Wait let's check again:

Simulations:

1. 506 - no
2. 619 - no
3. 535 - no
4. 769 - yes (1)
5. 096 - no
6. 380 - no
7. 527 - no
8. 555 - yes (2)
9. 737 - no
10. 192 - no
11. 092 - no
12. 658 - yes (3)
13. 694 - yes (4)
14. 320 - no
15. 442 - no
16. 812 - no
17. 968 - yes (5)
18. 765 - yes (6)
19. 374 - no
20. 282 - no

Ah, there are 6 simulations where all three flights are on - time. So the answer is D.6. Wait but maybe I made a mistake in the problem's number of simulations. But according to the check, the number of simulations with all on - time is 6.

Answer:

D. 6