The question asks if the given graph could represent a variable with a normal distribution, with reasoning based on the characteristics of the graph, and to estimate the mean and standard deviation if it is a normal distribution.

Analysis of the Options

1. Option A: "No, because the graph crosses the x-axis."

   • This is incorrect because normal distribution curves approach the x-axis asymptotically but do not cross it.

2. Option B: "No, because the graph is skewed right."

   • This is incorrect because the graph shown is symmetric, which is a key feature of a normal distribution. A skewed graph would not represent a normal distribution.

3. Option C: "No, because the graph is skewed left."

   • Similar to option B, this is incorrect as the graph is not skewed; it is symmetric.

4. Option D: "Yes, the graph fulfills the properties of the normal distribution. The mean is approximately ___ and the standard deviation is about ___."

   • This is the correct choice because the graph shown has the classic bell shape of a normal distribution, which is symmetric and unimodal.

Estimating Mean and Standard Deviation

From the graph:

• The peak (center) of the distribution appears around 20, suggesting the mean is approximately 20.
• The width of the curve from around 10 to 30 gives a range of roughly 20 units for two standard deviations (since about 95% of data in a normal distribution lies within two standard deviations).
• This suggests a standard deviation of around 5.

Answer

Correct Answer: Option D with the mean approximately 20 and standard deviation about 5.

Would you like further details on any part of this problem?

Related Questions

1. What characteristics define a normal distribution?
2. How can you visually estimate the standard deviation from a graph?
3. Why does a normal distribution never cross the x-axis?
4. What would indicate skewness in a graph like this one?
5. How can the empirical rule help in estimating mean and standard deviation?

Tip

When estimating the standard deviation from a normal curve, remember that the range of two standard deviations on either side of the mean covers approximately 95% of the data.