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The random variable X has a normal distribution with a mean
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30 Jul 2020, 11:26
30 Jul 2020, 11:26
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49% (01:28) correct
50% (01:21) wrong based on 292 sessions
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The random variable X has a normal distribution with a mean of 70.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Quantity A |
Quantity B |
The probability that \(− 30 ≤ X ≤ 150\) |
The probability that \(− 60 ≤ X ≤ 120\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
_________________
The random variable X has a normal distribution with a mean
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14 Jun 2021, 13:33
14 Jun 2021, 13:33
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Carcass wrote:
The random variable X has a normal distribution with a mean of 70.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The probability that \(− 30 ≤ X ≤ 150\) |
The probability that \(− 60 ≤ X ≤ 120\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
First notice that Quantities A and B both share the area under the curve between -30 and 120.
Now notice that the area between 120 and 150 is much greater than the area between -60 and -30.
So, Quantity A must be greater.
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Re: The random variable X has a normal distribution with a mean
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01 Aug 2020, 23:43
01 Aug 2020, 23:43
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The reason why option A is larger than B is because the interval of X given in A is tighter closer to the mean than the interval given in B.
Since there is more mass around the mean we have a greater probability.
-30<X<150
-60<X<120
Since the mean is 70. For option A you have an interval of length 100 to the left of the mean and an interval of length 80 to the right of the mean.
For option B you have an interval of length 130 to the left of the mean and an interval of length 50 to the right of the mean. So notice that for option A the intervals from both sides are more similar in length than in option B.
So this means even though option A and B are of the same length option B captures more mass further into the tails of the normal distribution's bell curve which carries very little probability. Option A captures more mass closer to the mean which carries more probability.
Since there is more mass around the mean we have a greater probability.
-30<X<150
-60<X<120
Since the mean is 70. For option A you have an interval of length 100 to the left of the mean and an interval of length 80 to the right of the mean.
For option B you have an interval of length 130 to the left of the mean and an interval of length 50 to the right of the mean. So notice that for option A the intervals from both sides are more similar in length than in option B.
So this means even though option A and B are of the same length option B captures more mass further into the tails of the normal distribution's bell curve which carries very little probability. Option A captures more mass closer to the mean which carries more probability.
General Discussion
Re: The random variable X has a normal distribution with a mean
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30 Jul 2020, 11:27
30 Jul 2020, 11:27
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Re: The random variable X has a normal distribution with a mean
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31 Jul 2020, 10:20
31 Jul 2020, 10:20
1
Why is A correct answer?
Is it because the length of both the intervals (-30 to 150 and -60 to 120) is same but the first one is more uniformly arranged about the mean?
Is it because the length of both the intervals (-30 to 150 and -60 to 120) is same but the first one is more uniformly arranged about the mean?
Re: The random variable X has a normal distribution with a mean
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31 Jul 2020, 10:26
31 Jul 2020, 10:26
Expert Reply
The mean of the distribution, 70, falls within both of those ranges. However, the range for Quantity B lies farther to the left side of the bell curve, therefore encompassing more of the tail of the normal distribution.
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Re: The random variable X has a normal distribution with a mean
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01 Aug 2020, 23:52
01 Aug 2020, 23:52
1
If anyone can explain with diagram plz
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Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!!
Re: The random variable X has a normal distribution with a mean
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02 Aug 2020, 00:05
02 Aug 2020, 00:05
3
Attachment:
bellCurves.PNG [ 20.27 KiB | Viewed 13477 times ]
Re: The random variable X has a normal distribution with a mean
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02 Aug 2020, 00:17
02 Aug 2020, 00:17
chacinluis wrote:
Attachment:
bellCurves.PNG
Thank you very much
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Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!!
Re: The random variable X has a normal distribution with a mean
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14 Jun 2021, 09:45
14 Jun 2021, 09:45
1
GreenlightTestPrep
Hi sir,
Can you please explain this question? How can we know which range is tighter around the mean if we don't have the standard deviation?
Thanks in advance!
Hi sir,
Can you please explain this question? How can we know which range is tighter around the mean if we don't have the standard deviation?
Thanks in advance!
Re: The random variable X has a normal distribution with a mean
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14 Jun 2021, 13:37
14 Jun 2021, 13:37
1
godxyz wrote:
GreenlightTestPrep
Hi sir,
Can you please explain this question? How can we know which range is tighter around the mean if we don't have the standard deviation?
Thanks in advance!
Hi sir,
Can you please explain this question? How can we know which range is tighter around the mean if we don't have the standard deviation?
Thanks in advance!
Done! (see above)
_________________
Re: The random variable X has a normal distribution with a mean
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28 Aug 2022, 09:12
28 Aug 2022, 09:12
1
Both intervals contain the numbers from -30 to 120, so they are the same in that regard, and we can ignore those values when comparing.
So what we need to compare is the interval 120 to 150 in option A versus the interval of -60 to -30 in option B. Both have a range of 30. However, the area under the normal curve (the "probability") is larger closer to the mean and smaller further away. So whichever of these intervals is closer to the mean of 70 will have a higher probability.
Option A is a distance of 50 to 80 from the mean (120-70 and 150-70) . Option B is a distance of 100 to 130 from the mean (70-(-30) and 70-(-60). So the normal curve is taller in the area between 120 and 150, since that is closer to the mean, thus the probability in that region is greater.
The answer is Option A.
So what we need to compare is the interval 120 to 150 in option A versus the interval of -60 to -30 in option B. Both have a range of 30. However, the area under the normal curve (the "probability") is larger closer to the mean and smaller further away. So whichever of these intervals is closer to the mean of 70 will have a higher probability.
Option A is a distance of 50 to 80 from the mean (120-70 and 150-70) . Option B is a distance of 100 to 130 from the mean (70-(-30) and 70-(-60). So the normal curve is taller in the area between 120 and 150, since that is closer to the mean, thus the probability in that region is greater.
The answer is Option A.
Re: The random variable X has a normal distribution with a mean
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13 Sep 2023, 13:28
13 Sep 2023, 13:28
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