Question

For test takers in a national level contest, the scores were observed to be normally distributed with a median score of 65 and a standard deviation of 4.

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

When dealing with probability distributions, knowing the mean and standard deviation is not always enough to determine the percentage without using a probability table or additional distribution data.

Answer 1

The Correct Option is D

In this problem, we are given a normal distribution with a median score of 65 and a standard deviation of 4. The quantity we need to compare is the percent of students with scores in the range 61 to 71. In a normal distribution: - The median score is 65, which is the center of the distribution. - A range of 61 to 71 represents a range of \( \pm 1 \) standard deviation from the mean. Since we don't have additional data (such as a normal distribution table or cumulative probabilities), we cannot definitively determine the percentage of students falling within this range without further information. Thus, the relationship cannot be determined from the given information.
Final Answer: \[ \boxed{\text{The relationship cannot be determined from the information given.}} \]