Question

Tests by an independent auditing firm show that 50% 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 1-5 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

Just look at each group. Does it have at least 3 alg lovers? How many groups have at least 3 algebra lovers? How many groups are there total?

Answer 2

I see it is a tricky question to interpret.

Altogether I see 3 different estimates here:

a) An estimate of 40% based on groups of 5. I think this is not the best estimate to use because the groups of 5 were selected randomly, so it can be assumed the students from the groups are independent. (See data below - I hope I counted everything right.)

b) An estimate using the binomial distribution with N=5, based on probability p=0.5 from the auditing firm, with k ≥ 3

k=3
5x4/2x1 = 10
p^3 = 1/8
q^2 = 1/4 -> 10/32
k=4
5 (1/2)^4(1/2) = 5/32
k=5 -> 1/32
total 16/32 = 1/2 (also can be seen using symmetry) Estimate is therefore 0.50 or 50%


c) An estimate using the binomial distribution with N=5, p=0.48 based on the 24 students seen in the data, with k ≥ 3

10 (0.48)^3 (0.52)^2 + 5(0.48)^4 (0.52)^1 + 1(0.48)^5 = 0.4625 approx.

I think the answer to give is 46%.


The most obvious step is to count the number of digits in each group of 5 that are in the set {1,2,3,4,5}.

12024 : 4 - 1224
55976 : 2 - 55
61475 : 3 - 145
70726 : 1 - 2
25408 : 3 - 254
62279 : 2 - 22
71874 : 2 - 14
03499 : 2 - 34
92659 : 2 - 25
26041 : 3 - 241

The following information is counted and added up:
Number of groups actually having at least three Algebra lovers: 4
Number of groups: 10
Number of students: 50
Number of students who love algebra: 24

(Generally in stories like this you believe what it says about the auditing firm's results. In real life you'd try to be sure to check the auditing firm's credentials, rep, and process somewhat. They may get testy if you try to check their process too much, because they are protecting their profession so they can continue to get paid and to be friends with other members of their profession).

Answer 3

Holy freaking crap, Zhang.

Answer 4

what @SmoothMath

Answer 5

Wow thank you for your help, so would it be 50% or 46%?

Answer 6

You should publish that response as a novel.

Answer 7

@SmoothMath lol i should i love do novel

@CZS93 Which do you think it was 50% or 46 %

Answer 8

I am unsure, I can't imagine it would be exactly 50%. Although you are the one that knew the whole process on how to do this question.

Answer 9

ok CZS93 reread what i just wrote and think about it and you'll know which one is the answer.

Answer 10

I am going with 46%

Answer 11

that is correct :)

Answer 12

need any more help?

Answer 13

I have one last question if you could help me please?

Answer 14

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If a certain statistician has an IQ of 122, what percent of the population has an IQ less than she does?

A. 7%
B. 22%
C. 93%
D. 99%
E. 47%

Answer 15

99.6% for apex so it would be D

Answer 16

Darn, it said it was wrong:(

Answer 17

which one...

Answer 18

The last one I asked..