Determine whether the graph shown could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![**Educational Content: Understanding Normal Distributions**
**Topic: Determining the Normalcy of Graphs**
In this exercise, you are asked to determine whether a given graph could represent a variable with a normal distribution. If it appears to be normally distributed, you should estimate the mean and standard deviation.
**Graph Description:**
- The graph depicted is a curve plotted on a grid with the x-axis labeled at intervals ranging from 36 to 60.
- The curve appears bell-shaped and peaks around the middle of the x-axis.
**Question and Options:**
*Determine whether the graph shown could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.*
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
- **Option A**: The graph could not represent a variable with a normal distribution because the curve crosses the x-axis.
- **Option B**: The graph could not represent a variable with a normal distribution because the curve is constant.
- **Option C**: The graph could represent a variable with a normal distribution because the curve is symmetric and bell-shaped. Its mean is approximately [Box], and its standard deviation is approximately [Box]. (Round to one decimal place as needed.)
**Instructions:**
Click to select and enter your answer(s). Consider the symmetry and shape of the curve when making your decision.
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*Note: An understanding of normal distributions is important for interpreting statistical data, making this a fundamental skill in statistical analysis.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc04ad377-fa18-4d76-a07f-c97e24df23ae%2F1fde3c0e-7caf-4a2b-a547-e5e94a69c698%2Fr5xmq8d_processed.jpeg&w=3840&q=75)
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