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Director  Joined: 29 Nov 2012
Posts: 696
The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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1
28 00:00

Difficulty:   35% (medium)

Question Stats: 70% (02:12) correct 30% (02:28) wrong based on 399 sessions

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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

Attachment: DSCN0392.JPG [ 1002.27 KiB | Viewed 5261 times ]

Originally posted by fozzzy on 08 Jan 2013, 21:25.
Last edited by fozzzy on 09 Jan 2013, 03:43, edited 1 time in total.
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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14
1
3
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
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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?
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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7
1
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 between 1 and 7 inclusive as  [#permalink]

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2
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 _________________
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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 between 1 and 7 inclusive as  [#permalink]

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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
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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 between 1 and 7 inclusive as  [#permalink]

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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...
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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3
x has values between 1 and 7 so $$|4-x|>\frac{3}{2}$$=

|4-1|=3>3/2
|4-2|=2>3/2
|4-3|=1>3/2
|4-4|=0>3/2
|4-5|=1>3/2

|4-6|=2>3/2
|4-7|=3>3/2

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 $$\frac{8}{15}$$
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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? Director  Joined: 29 Nov 2012
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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 x will 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
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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.
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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.
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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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?"
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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Hi,

Can someone explain why we have considered frequencies while the stem asks us about the value of X?

I mean, the probability of abs (4-X) >1.5 , then what values of X can be considered ?

Or did i miss something?
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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1
Q - 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?

i.e |x - 4 | > 3 / 2

according to absolute value rules above equation becomes.

x-4 > 3 / 2 and x-4 < -3/2

solving both - we get : x > 5.5 and x < 2.5.

from the table we have - 6 ,7 ,7 7 above 5.5 and 2 , 1 ,1 ,1 below 2.5 . total - 8 occurrences.

probability = number of occurrences / total occurrences

P = 8 / 15

Ans - 8 / 15

Thanks.
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Re: The variable x takes on integer values between 1 and 7 inclusive as  [#permalink]

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Woody19 wrote:
Q - 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?

i.e |x - 4 | > 3 / 2

according to absolute value rules above equation becomes.

x-4 > 3 / 2 and x-4 < -3/2

solving both - we get : x > 5.5 and x < 2.5.

from the table we have - 6 ,7 ,7 7 above 5.5 and 2 , 1 ,1 ,1 below 2.5 . total - 8 occurrences.

probability = number of occurrences / total occurrences

P = 8 / 15

Ans - 8 / 15

Thanks.

Just what I was looking for! I was breaking my head as to how are they including 6 and 7 as well since x < 2.5. But what I missed was that the "absolute value", hence x < 2.5 and x>5.5 must be taken into consideration.

Thank you so much!
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Help needed to get to a score of 700+ I'm at all ears!! Re: The variable x takes on integer values between 1 and 7 inclusive as   [#permalink] 08 Jun 2019, 01:59
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