GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The random variable X has a normal distribution with a mean
[#permalink]
30 Jul 2020, 11:26
30 Jul 2020, 11:26
Expert Reply
32
Bookmarks
00:00
Question Stats:
48% (01:32) correct
51% (01:23) wrong based on 374 sessions
Hide Show timer Statistics
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
The random variable X has a normal distribution with a mean
[#permalink]
14 Jun 2021, 13:33
14 Jun 2021, 13:33
6
1
11
Bookmarks
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.
Re: The random variable X has a normal distribution with a mean
[#permalink]
01 Aug 2020, 23:43
01 Aug 2020, 23:43
5
1
Bookmarks
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.
