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23 votes
Use the table of random numbers to simulate the situation.

On an average, 45% of the students in a college take a computer
course. Estimate the probability that at least 6 of the next 10
students will take a computer course.
48095
24765
05604
46497
11966
93354
86431
34731
56521
69722
26295
79423
42669
70962
17355
29826
53442
68241
88383
26431
73434
53041
29591
58166
23544
61132
12955
22834
41592
64119
53147
33205
82873
70967
70034
47821
11153
02989
37977
93425
O Possible answer: 60%
O Possible answer: 50%
O Possible answer: 55%
O Possible answer. 45%

2 Answers

4 votes

Answer:50%

Step-by-step explanation:believe me it is 50%. 40% isn’t even a option. 50% is the correct answer.

User Bekce
by
3.8k points
6 votes

Answer:

  • 40%

Explanation:

A set of random numbers can be used for simulating a situation by defining how the numbers will be used to represent the possible outcomes. Trials are repeated using newly-generated random numbers until there are a sufficient number of trials to give a reasonable prediction of the probability of interest.

__

We can simulate the situation as follows:

  • if a pair of digits is in the range 00-44, then the student will be taking a computer course
  • a sequence of 10 pairs of digits (4 of the 5-digit numbers) will represent a group of 10 students
  • We are interested in the fraction of groups of 10 that have 6 or more that take a computer course. (Theoretical probability is about 26%.)

Here are our trials and results.

48 09 52 47 65 05 60 44 64 97 -- 3 of 10

11 96 69 33 54 86 43 13 47 31 -- 5 of 10

56 52 16 97 22 26 29 57 94 23 -- 5 of 10

42 66 97 09 62 17 35 52 98 26 -- 5 of 10

53 44 26 82 41 88 38 32 64 31 -- 6 of 10

73 43 45 30 41 29 59 15 81 66 -- 5 of 10

23 54 46 11 32 12 95 52 28 34 -- 6 of 10

41 59 26 41 19 53 14 73 32 05 -- 7 of 10

82 87 37 09 67 70 03 44 78 21 -- 5 of 10

11 15 30 29 89 37 97 79 34 25 -- 7 of 10

__

Of these 10 trials, 4 showed the result that at least 6 of the next 10 students will choose a computer course. That is, the probability is estimated to be about 4/10 = 40%.

_____

Additional comment

Here, we can only predict the probability of interest as some multiple of 10%, since we have numbers sufficient for only 10 trials.

We could arrange the random numbers a different way and reuse them, but we choose not to for the purpose of this answer. For that to make sense, we need to have assurance that these numbers are truly random.

The number of repeated values among these 100 pairs of digits suggests that this is a poor set of numbers to be using. 26 and 41 each show up 4 times, for example. The probability of that happening by chance in a truly random set of numbers is about 0.03%. A chance event is considered to be unlikely if its probability is less than 1%.

User Iman Akbari
by
3.9k points