Questions: 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. A. The graph could not represent a variable with a normal distribution because the graph is skewed to the left. B. The graph could not represent a variable with a normal distribution because the curve crosses the x-axis. C. The graph could not represent a variable with a normal distribution because the graph is skewed to the right. D. The graph could not represent a variable with a normal distribution because the curve is constant. E. The graph could represent a variable with a normal distribution because the curve is symmetric and bell-shaped. Its mean is approximately , and its standard deviation is approximately ?. (Round to one decimal place as needed) F. The graph could not represent a variable with a normal distribution because the curve has two modes

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. A. The graph could not represent a variable with a normal distribution because the graph is skewed to the left. B. The graph could not represent a variable with a normal distribution because the curve crosses the x-axis. C. The graph could not represent a variable with a normal distribution because the graph is skewed to the right. D. The graph could not represent a variable with a normal distribution because the curve is constant. E. The graph could represent a variable with a normal distribution because the curve is symmetric and bell-shaped. Its mean is approximately , and its standard deviation is approximately ?. (Round to one decimal place as needed) F. The graph could not represent a variable with a normal distribution because the curve has two modes
Transcript text: 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. A. The graph could not represent a variable with a normal distribution because the graph is skewed to the left. B. The graph could not represent a variable with a normal distribution because the curve crosses the $x$-axis. C. The graph could not represent a variable with a normal distribution because the graph is skewed to the right D. The graph could not represent a variable with a normal distribution because the curve is constant. E. The graph could represent a variable with a normal distribution because the curve is symmetric and bell-shaped. Its mean is approximately $\square$ , and its standard deviation is approximately $\square$ ?. (Round to one decimal place as needed) F. The graph could not represent a variable with a normal distribution because the curve has two modes
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Solution

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Solution Steps

Step 1: Analyze the Graph

The graph provided appears to be symmetric and bell-shaped, which are key characteristics of a normal distribution.

Step 2: Evaluate the Options
  • Option A: The graph is not skewed to the left.
  • Option B: The graph does cross the x-axis, but this is typical for a normal distribution.
  • Option C: The graph is not skewed to the right.
  • Option D: The graph is not constant; it has a peak and tails.
  • Option E: The graph is symmetric and bell-shaped, indicating it could represent a normal distribution.
  • Option F: The graph does not have two modes; it has a single peak.
Step 3: Estimate the Mean and Standard Deviation
  • Mean: The mean of a normal distribution is located at the peak of the bell curve. From the graph, the peak appears to be at \( x = 4 \).
  • Standard Deviation: The standard deviation can be estimated by observing the spread of the data. The points where the curve changes concavity (inflection points) are approximately one standard deviation away from the mean. These points appear to be at \( x = 3 \) and \( x = 5 \), suggesting a standard deviation of approximately \( 1 \).

Final Answer

The graph could represent a variable with a normal distribution because the curve is symmetric and bell-shaped. Its mean is approximately \( 4 \) and its standard deviation is approximately \( 1 \).

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