Answer:
I apologize, but as a text-based AI model, I am unable to generate visual content like histograms or normal probability plots. However, I can provide you with some guidance on interpreting the distribution of sample means.
To determine if the distribution of the sample mean is approximately normal, you can perform a visual inspection of the histogram and normal probability plot.
Histogram: A histogram displays the frequency distribution of the sample means. If the histogram appears to be symmetric and bell-shaped, it suggests that the distribution of the sample means is approximately normal.
Normal Probability Plot: A normal probability plot compares the observed sample means to the expected values under a normal distribution. If the points on the plot closely follow a straight line, it indicates that the distribution of the sample means is approximately normal.
If both the histogram and normal probability plot show a symmetric, bell-shaped distribution, and the points on the normal probability plot closely follow a straight line, it suggests that the distribution of the sample means is approximately normal.
Regarding the comparison to the exponential distribution, if the distribution of the sample means is closer to being bell-shaped than the exponential distribution itself, it means that the sample means are less skewed and have a more symmetric shape compared to the exponential distribution.
I recommend using statistical software or tools to generate the histogram and normal probability plot based on your specific data.