What does the area under the curve of the normal distribution represent?

Question

BlackTom AI · Accepted Answer

The question asks what the area under the curve of the normal distribution represents.
Option 1: 'The probability of obtaining any of a given range of values.' This is correct in the sense that the area under the curve over an interval corresponds to the probability that a value drawn from the distribution falls within that interval. It captures the fundamental link between probability and geometry on the PDF.
Option 2: 'The probability of obtaining the highest value in a specified range.' This is too specific and misleading; while the area over a whole interval can include high values, probability is distributed across the entire range and is not limited to just the highest value unless the interval is defined that way. It misstates the general relationship.
Option 3: 'The probability of obtaining the lowest value in a specified range.' Similar to option 2, it fixes attention on a single extreme value. Probabilities over a range are represented by the total area of that range, not only the lowest value. This choice mischaracterizes how probability accumulates over an interval.
Option 4: 'The probability that the mean of a population exists in a specified range.' This is incorrect because the mean is a parameter of the distribution, not a random value drawn from the distribution in a single observation. The area under the curve concerns the probability of individual observations, not the location of the mean itself.

PSYC20007_2025_SM2 Goals of Statistical Testing II

What does the area under the curve of the normal distribution represent?

查看解析

登录即可查看完整答案

类似问题

X~N(3, 1) and Y~N(3, 2), then

Question at position 50 A soft-drink machine can be regulated so that it discharges an average of ? oz per cup. If the ounces of fill are Normally distributed with a standard deviation of 0.4 oz, what should ? be set at so that 98% of the 6-oz cups will not overflow?6.606.826.006.185.18

In a normal distribution where X ~N(0,1) , approximately what is the probability that X is between -1 and 0.

Suppose that the number of credit hours a student takes follows a normal distribution with a mean of 17 credit hours and a standard deviation of 2 credit hours. A normal course load is between 12 and 19 hours. What proportion of students have a normal course load?

The mean height of a bull population is 150cm. The population shows a normal distribution with a standard deviation of 7cm. What will be the maximum height of bulls that are within 2 standard deviations of the mean?

Is BaP response-frequency approximately normally distributed with respect to log(dose)?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单