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Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.
Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.
Quantity A: The value at the 75th percentile of the distribution of X
Quantity B: 750
(d)The relationship cannot be determined from the information given.
- a)Quantity A is greater.
- b)Quantity B is greater.
- c)The two quantities are equal.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Directions: Compare Quantity A and Quantity B, using additional infor...
Given information:
- Random variable X is normally distributed.
- The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.
To find:
Compare Quantity A and Quantity B.
Quantity A: The value at the 75th percentile of the distribution of X.
Quantity B: 750.
Approach:
To compare Quantity A and Quantity B, we need to determine the value at the 75th percentile of the distribution of X.
Solution:
A normal distribution is symmetric, meaning that the percentiles are evenly distributed on both sides of the mean. Since the mean is not given, we can assume it to be the midpoint between 650 and 850, which is (650 + 850)/2 = 750.
To find the value at the 75th percentile, we can use the property that approximately 68% of the data lies within one standard deviation of the mean, and about 95% lies within two standard deviations. This means that the 75th percentile is closer to the mean than the 90th percentile.
Explanation:
The value at the 75th percentile of the distribution of X is closer to the mean (750) than the value at the 90th percentile (850). Therefore, Quantity A is greater than Quantity B.
Answer:
Quantity A is greater. (Option a)
- Random variable X is normally distributed.
- The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.
To find:
Compare Quantity A and Quantity B.
Quantity A: The value at the 75th percentile of the distribution of X.
Quantity B: 750.
Approach:
To compare Quantity A and Quantity B, we need to determine the value at the 75th percentile of the distribution of X.
Solution:
A normal distribution is symmetric, meaning that the percentiles are evenly distributed on both sides of the mean. Since the mean is not given, we can assume it to be the midpoint between 650 and 850, which is (650 + 850)/2 = 750.
To find the value at the 75th percentile, we can use the property that approximately 68% of the data lies within one standard deviation of the mean, and about 95% lies within two standard deviations. This means that the 75th percentile is closer to the mean than the 90th percentile.
Explanation:
The value at the 75th percentile of the distribution of X is closer to the mean (750) than the value at the 90th percentile (850). Therefore, Quantity A is greater than Quantity B.
Answer:
Quantity A is greater. (Option a)
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Community Answer
Directions: Compare Quantity A and Quantity B, using additional infor...
You are given that the distribution of random variable X is normal and that the values 650 and 850 are at the 60th and 90th percentiles of the distribution, respectively.
Both of the values 650 and 850 are greater than the mean of the distribution. If you draw a rough sketch of the graph of the normal distribution, the sketch could look something like the one below. Note that it is not necessary to know the exact location of 650 and 850, just that both values are above the mean.
To say that the value 650 is at the 60th percentile of the distribution means, graphically, that 60 percent of the area between the normal curve and the horizontal axis lies to the left of the vertical line segment at 650. To say that 850 is at the 90th percentile of the distribution means that 90 percent of the area between the normal curve and the horizontal axis lies to the left of the vertical line segment at 850.
The value 750 is halfway between 650 and 850. However, because the curve is decreasing in that interval, the area between 650 and 750 is greater than the area between 750 and 850. Since the value at the 75th percentile should divide in half the area between the value at the 60th percentile (650) and the value at the 90th percentile (850), this value is closer to 650 than to 850. Thus you can conclude that Quantity A, the value at the 75th percentile of the distribution of X, is less than Quantity B. The correct answer is Choice B.
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Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer?
Question Description
Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer?.
Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices. A symbol that appears more than once in a question has the same meaning throughout the question.Q. The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.Quantity A: The value at the 75th percentile of the distribution of XQuantity B: 750(d)The relationship cannot be determined from the information given.a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GRE.
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