Question

Tests by an independent auditing firm show that 60% of students in a certain school think that Algebra is the best course they have ever taken. Use the entire line of random numbers below to estimate the probability that a randomly selected group of five students will contain at least 3 Algebra lovers. Let the digits 1-6 represent a student who thinks that Algebra is the best course.

12024 55976 61475 70726 25408 62279 71874 03499 92659 26041

Convert your probability answer to a whole number representing a percent.

Answer 1

Interesting. There are 50 numbers in the list, so I think you are supposed to treat each group of 5 numbers as a sample, which gives you 10 samples. From that you can see the proportion of samples that contain at least 3 algebra lovers. Note that this probability will be a multiple of 10% (since there are 10 samples, each one either does or does not have 3 algebra lovers).

I THINK that's what the problem is getting at?

Answer 2

im confused

Answer 3

So e.g., 1= has at least 3 algebra lovers, 0=doesn't.

12024 (1) since 1,2,2,4 are all algebra lovers.
55976 (1) since 5,5,6
61475 (1)
70726 (0) since only 2,6
25408
62279
71874
03499
92659
26041

Get the idea? Go down the list, and each sample either does or does not have at least 3 algebra lovers.

You are using the random numbers, and the fact that p=0.6, to simulate drawing 10 samples.

Answer 4

7 of them have at least 3 algebra lovers

Answer 5

3 of them dont have at least 3

Answer 6

7/10

Answer 7

so .70 wpuld be the answer?

Answer 8

the answer is 70

Answer 9

Divide the random numbers into 5 sets 10 of numbers each and count the number of digits from 1 to 6 inclusive in each set:
Random number Number of digits from 1 ~ 6
12024 55976 7
61475 70726 7
25408 62279 6
71874 03499 4
92659 26041 7
Note that the numbers from 1 to 6 inclusive represent 60% of the digits from 0 to 9.
Now get the total number of digits from 1 to 6 in the sample of 5:
7 + 7 + 6 + 4 + 7 = x
and divide x by 5 to find the average 'score' out of 10 for the sample of 5 students.
The required percentage is then
\[\frac{x}{5}\times\frac{100}{10}=you\ can\ calculate\]