Three questions: 1) The distribution of hourly income in a

Question

Three questions:

1) The distribution of hourly income in a certain company is as follows:

 # People   Hourly Income 

10 150
20 125
20 100
30 50
15 20

What is the median Hourly income?

2) There are a group of 3 men and 3 women. A committe of 4 is to be formed consisting of EQUAL numbers of men and women. What is the probability of forming a committee consisting of EQUAL numbers of men and women?

3) The distribution of ages in a class is as follows:

 #Students   Age 

1) 2 7
2) 5 10
3) 3 12

The SD lies between x and y. What are x and y?

Note: I dont have answers to these questions.

sofere · Answer

Still workin on #2, but this is how you do #1 & #3.

#1
There are a total of 95 people (10+20+20+30+15). The median is the is person # (n+1)/2 ...(95+1)/2 = 48. The median is the 48th person when listed in order of hourly rate. There are 15 people at $15/hr or less... 15+30 or 45 people at $50/hr or less, and 15+30+20 or 65 people at $100/hr or less. Person #48 must therefore be making $100/hr. The median hourly income is $100/hr.

#3
Std deviation is the square root of the sum of the square of the differences btwn x and the mean.

The mean is equal to  /(2+5+3) = 100/10 = 10

The sum of the square of the differences from the mean is 2* +5* +3*  = 2*9 + 3*4 = 30

The std. dev is the sqrt(30) which is btwn sqrt(25) and sqrt(36), therefore the std. dev lies btwn 5 and 6. x = 5 and y = 6.

sofere · Answer

#2

The only way there can be an equal number of men and women is if there are 2 men and 2 women
Rephrase the question...what are the chances that 2 men and 2 women are chosen for the commitee.

In order to find the probability we must find the number of combos where you can have 2 men and 2 women and divide it by the total number of possible 4 person groups.

# of combos with 2 men and 2 women:
This is basically the number of possible 2 men groups * the number of possible 2 woman groups or 3*2 * 3*2 = 6*6 = 36
# of combos of 4 person groups
6 total people for 4 spots...6*5*4*3 = 360.

The chance of having a group with equal # of men and women is 36/360 or 1/10.

Please check my work, its been a while since i've done permutations and combos.

twixt · Answer

These questions are really weird...

I do not understand the first one, my assessment of median = 80,1 usd/h, maybe you did not put enough data to understand the distribution scheme

To me answer to Q2 is 1/2, this pb is symmetrical

Q3 : same point as Q1, wordy, SD has only 1 value, anyway above approach looks good.

Anonymous · Answer

sofere, I too got the same answers to #1 and #2.

twixt · Answer

I think we need a prob guru here...

I re-read the stem and my solution is :

2W+2M : 3C2.3C2

Total comb : 6C4

prob = 9/15 = 3/5

Others comb : 1M+3W = 1W+3M = 3C3.3C1 = 3

sofere · Answer

You are correct. I think I was using permutations instead of combinations. 

Should be  /(6!/4!2!) = (3*3)/15 = 9/15.

sofere · Answer

Not quite sure where you got 80 from.

If we scale down the question we can list everything out so i'm gonna divide the # of people by 5.

People....Hourly Income
2............150
4............125
4............100
6............50
3............20

So the hourly incomes listed out are 
{20,20,20,50,50,50,50,50,50,100,100,100,100,125,125,125,125,150,150}

The middle number is the 10th one in, or 100.

I prefer the method in my first explanation, but this is just a way to visualize it.

boksana · Answer

#2 the answer is 3/5

hardworker_indian · Answer

1. What is the median Hourly income?  
100.hr. Agree with sofere's method.

 2. I will rephrase the question.
There are a group of 3 men and 3 women. A committe of 4 is to be formed. What is the probability of forming a committee consisting of EQUAL numbers of men and women? 

Pb of total events = 6C4 = 15
Pb of fav events = 3C2.3C2 = 9
Pb = 9/15 = 3/5

 3. The SD lies between x and y. What are x and y?  
Agree with sofere's method, I made some midifications.

Std deviation is the square root of the sum of the square of the differences btwn x and the mean.
The mean is equal to  /(2+5+3) = 100/10 = 10
The sum of the square of the differences from the mean is 2* +5* +3*  = 2*9 + 3*4 = 30
 Ave of square of differences = 30/10 = 3
therefore the std. dev lies btwn 1 and 2 x = 1 and y = 2. 

Am I right in the third?

sofere · Answer

Aww, crap on a stick...I forgot to divide by n.

Why do i always forget to divide by n :madd 

Thanks for the correction H.W. Indian

Three questions: 1) The distribution of hourly income in a

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