A normal distribution is a bell-shaped curve with a majority of the cases falling within the
Blank
______ of the range.

Question

A normal distribution is a bell-shaped curve with a majority of the cases falling within the 
Blank
______ of the range.

BlackTom AI · Accepted Answer

A normal distribution is symmetric about its mean, so the majority of cases are concentrated in the middle of the range.

1. Relevant knowledge points and concepts
- Normal (Gaussian) distribution: bell-shaped, symmetric around the mean; mean = median = mode.
- Empirical (68–95–99.7) rule: about 68% of observations lie within ±1 standard deviation (σ) of the mean, about 95% within ±2σ, and about 99.7% within ±3σ.
- "Majority" means more than 50% of observations.

2. Step-by-step reasoning
- Because the curve is symmetric, the center (mean) is where data are densest.
- Use the empirical rule to quantify "majority": within ±1σ of the mean is considered the central/middle portion.
- Since 68% > 50%, a majority of observations are in that central region.

3. Calculations and intermediate steps
- Total percentage within ±1σ = 68% (empirical rule).
- Percentage outside ±1σ = 100% − 68% = 32%, split equally into two tails: 16% in the left tail beyond −1σ and 16% in the right tail beyond +1σ.
- Therefore central (middle) portion contains a clear majority (68%).

4. Why the correct answer is correct
- The definition and empirical rule show that most observations cluster at the center of the bell curve; numerically, 68% (a majority) lie in the middle region, so "middle" correctly describes where the majority fall.

5. Why other options are incorrect
- "Extreme left" and "left": tails on either side contain relatively small percentages (e.g., 16% beyond −1σ), so they are not where the majority lie.
- "Right": similarly, the right tail holds a minority, not the majority.
- Only "middle" fits both the descriptive shape and the quantitative empirical rule.

6. Conclusion
The correct answer is "middle," which matches the provided answer.

A normal distribution is a bell-shaped curve with a majority of the cases falling within the Blank ______ of the range.单项选择题

类似问题

A bell-shaped probability curve demonstrates a(n) Blank ______ distribution.

The tensile strength of paper can be modelled by a normal distribution with a mean of 240kPa and standard deviation 15kPa. What proportion of paper produced will fail specifications, if the paper must have strength of at least 225kPa?

The tensile strength of paper can be modelled by a normal distribution with a mean of 240kPa and standard deviation 15kPa. What is the probability that the tensile strength will be between 226kPa and 243kPa?

Select the MOST appropriate statement for the population parameters of the Normal distribution shown below

The average length of a dog pregnancy is a normal random variable with mean 𝜇 = 63 days and standard deviation 𝜎 = 5 days. Use the empirical rule to determine what percent of dogs are pregnant longer than 68 days.

The hatching weights of commercial chicks can be modeled using a normal distribution with a mean of 45 grams and standard deviation of 4 grams. What is the probability that a randomly selected chick weighs between 33 and 41 grams?

更多留学生实用工具

智能学习助手

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