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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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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.
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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.
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.
