Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall?
A) 0.75
B) 0.50
C) 0.25
D) 0.17

Question

Quizplus · Accepted Answer

Using the properties of a normal distribution, we know that approximately 68% of the data falls within one standard deviation of the mean. Since the question asks for the proportion of women between 65 and 67 inches tall, we are looking at the range from the mean to one standard deviation above the mean. This range captures about half of the 68%, which is approximately 34%. However, the closest option to 34% is 25% (option C), indicating a slight misunderstanding in the direct application of the rule. The correct interpretation should consider that the exact proportion in this specific range can be more accurately found using the standard normal distribution table or Z-scores, which would typically show that the area from the mean to one standard deviation above encompasses slightly less than 34%. However, without precise calculation tools or options that closely match the expected percentage, the best estimate given the options would be around 34%, suggesting a need for clarification in the answer choices provided.

Heights of College Women Have a Distribution That Can Be