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The variable x takes on integer values between 1 and 7 inclu [#permalink]
08 Jan 2013, 20:25

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Difficulty:

45% (medium)

Question Stats:

72% (01:57) correct
28% (01:42) wrong based on 116 sessions

X frequency 1 3 2 1 3 3 4 1 5 3 6 1 7 3

The variable x takes on integer values between 1 and 7 inclusive as shown above. What is the probability that the absolute value of the difference between the mean of the distribution which is 4 and a randomly chosen value of x will be greater than 3/2?

Re: The variable X takes on integer values [#permalink]
08 Jan 2013, 21:58

3

This post received KUDOS

bhavinshah5685 wrote:

MacFauz wrote:

The set is 1,1,1,2,3,3,3,4,5,5,5,6,7,7,7

The question basically asks for the probability of choosing 1,2,6 or 7.

= 8/15

Hi Can you please explain in detail?

how u got the values of set?

Looking at the table.,

The column on the left shows the value of X and the column on the right shows the number of times the value appears. The question statement is just beating around the bush a lot to ask a simple question. What is the probability that 4 - X > 1.5. For such a case, X has to be 1,2,6 or 7. _________________

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Re: The variable X takes on integer values [#permalink]
09 Jan 2013, 19:47

MacFauz wrote:

bhavinshah5685 wrote:

MacFauz wrote:

The set is 1,1,1,2,3,3,3,4,5,5,5,6,7,7,7

The question basically asks for the probability of choosing 1,2,6 or 7.

= 8/15

Hi Can you please explain in detail?

how u got the values of set?

Looking at the table.,

The column on the left shows the value of X and the column on the right shows the number of times the value appears. The question statement is just beating around the bush a lot to ask a simple question. What is the probability that 4 - X > 1.5. For such a case, X has to be 1,2,6 or 7.

Hi MacFauz, I guess answer is correct but the solution seems to be different to me. Pls correct me!

given absolute difference is |4-X| >1.5 so -1.5> |4-X| >1.5 solving this 2.5 < X < 6.5 This gives range from 3,3,3,4,5,5,5,6

Anyways, answer will be 8/15.

Actually i did this wrong. On seeing ur solution i got it _________________

GMAT - Practice, Patience, Persistence Kudos if u like

Re: The variable X takes on integer values [#permalink]
09 Jan 2013, 20:27

shanmugamgsn wrote:

MacFauz wrote:

bhavinshah5685 wrote:

The set is 1,1,1,2,3,3,3,4,5,5,5,6,7,7,7

The question basically asks for the probability of choosing 1,2,6 or 7.

= 8/15

Hi Can you please explain in detail?

how u got the values of set?

Looking at the table.,

The column on the left shows the value of X and the column on the right shows the number of times the value appears. The question statement is just beating around the bush a lot to ask a simple question. What is the probability that 4 - X > 1.5. For such a case, X has to be 1,2,6 or 7.

Hi MacFauz, I guess answer is correct but the solution seems to be different to me. Pls correct me!

given absolute difference is |4-X| >1.5 so -1.5> |4-X| >1.5 solving this 2.5 < X < 6.5 This gives range from 3,3,3,4,5,5,5,6

Anyways, answer will be 8/15.

Actually i did this wrong. On seeing ur solution i got it

The step in red is incorrect. You should note that the least value that |4-X| can take is 0. So, it can never be less than -1.5. The inequality should actually be X<2.5 or X>5.5. _________________

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Re: The variable X takes on integer values [#permalink]
09 Jan 2013, 21:58

shanmugamgsn wrote:

Actually it should be -1.5> 4-X >1.5 (it was a typo above)

But still i didnt get u! |4-X| can be zero ? then |4-X|>1.5 will be 0>1.5

This isnt wrong?

Messed up Pls explain

I guess I wasn't clear. What I meant to say was that a modulus value cannot be negative. Of course in this question, we want only values for which |4-X|>1.5. The range that you have given (-1.5> 4-X >1.5) is not a valid one. A number cannot be both greater than 1.5 and lesser than -1.5. Rather the interval should be 1.5 < 4-X OR 4-X < -1.5 _________________

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Re: The variable X takes on integer values [#permalink]
10 Jan 2013, 19:05

MacFauz wrote:

shanmugamgsn wrote:

Actually it should be -1.5> 4-X >1.5 (it was a typo above)

But still i didnt get u! |4-X| can be zero ? then |4-X|>1.5 will be 0>1.5

This isnt wrong?

Messed up Pls explain

I guess I wasn't clear. What I meant to say was that a modulus value cannot be negative. Of course in this question, we want only values for which |4-X|>1.5. The range that you have given (-1.5> 4-X >1.5) is not a valid one. A number cannot be both greater than 1.5 and lesser than -1.5. Rather the interval should be 1.5 < 4-X OR 4-X < -1.5

Thanks MacFauz... ya i got my mistake in Inequalities. Thanks dude... _________________

GMAT - Practice, Patience, Persistence Kudos if u like

The value that respect |4-x|>3/2 are 1,2,6,7 that have a frequency of 3,1,1,3 so 3+1+1+3 = total frequencies of "right" events, and this will be our numerator. Our denominator will be the tot number of combinations = 3+1+3+1+3+1+3= 15. Answer \frac{8}{15} _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: The variable x takes on integer values between 1 and 7 inclu [#permalink]
18 Jul 2013, 02:44

I have a question regarding the denominator 15 : why do we take into consideration the value 4 since it occurs only once and we're looking for the the difference between this value and the others. I had the answer wrong because I assumed the denominator was 14 - could someone try to explain?

Re: The variable x takes on integer values between 1 and 7 inclu [#permalink]
18 Jul 2013, 06:50

aa81 wrote:

I have a question regarding the denominator 15 : why do we take into consideration the value 4 since it occurs only once and we're looking for the the difference between this value and the others. I had the answer wrong because I assumed the denominator was 14 - could someone try to explain?

The question states

What is the probability that the absolute value of the difference between the mean of the distribution which is 4 and a randomly chosen value of xwill be greater than 3/2?

you get 15 when you add the frequency ( 3+1+3 etc)

The set is

The set is 1,1,1,2,3,3,3,4,5,5,5,6,7,7,7 _________________

Re: The variable x takes on integer values between 1 and 7 inclu [#permalink]
18 Jul 2013, 07:41

fozzzy wrote:

X frequency 1 3 2 1 3 3 4 1 5 3 6 1 7 3

The variable x takes on integer values between 1 and 7 inclusive as shown above. What is the probability that the absolute value of the difference between the mean of the distribution which is 4 and a randomly chosen value of x will be greater than 3/2?

A) 8/15 B) 4/7 C) 4/5 D) 6/7 E) 8/7

How can the probability of doing something be 3/2?

How can the probability of doing something be greater than 1?

I don't understand what y'all are calculating. _________________

Re: The variable x takes on integer values between 1 and 7 inclu [#permalink]
18 Jul 2013, 08:35

fozzzy wrote:

knightofdelta wrote:

How can the probability of doing something be 3/2?

How can the probability of doing something be greater than 1?

I don't understand what y'all are calculating.

The final answer is below 1

8/15 = 0.5333

Then the answer should be 0 since the answer will be below 3/2. 3/2 is higher than 1 and the answer is below 1. Therefore, since the answer is certainly below 1 and 1 is below 3/2, then the answer is 0. And 0 is not one of the answer choices.

Summary: the question is faulty. _________________

Re: The variable x takes on integer values between 1 and 7 inclu [#permalink]
21 Jul 2013, 01:41

Expert's post

knightofdelta wrote:

fozzzy wrote:

knightofdelta wrote:

How can the probability of doing something be 3/2?

How can the probability of doing something be greater than 1?

I don't understand what y'all are calculating.

The final answer is below 1

8/15 = 0.5333

Then the answer should be 0 since the answer will be below 3/2. 3/2 is higher than 1 and the answer is below 1. Therefore, since the answer is certainly below 1 and 1 is below 3/2, then the answer is 0. And 0 is not one of the answer choices.

Summary: the question is faulty.

Please read the question carefully. The question asks "what is the probability that SOME VALUE will be greater than 3/2?" not "is the probability of SOME EVENT greater than 3/2?" _________________