Final answer:
To draw histograms for two variables with the same mean but different variances, plot two bell-shaped curves centered at the mean; the one with lower variance will be taller and narrower, while the higher variance will be broader and flatter.
Step-by-step explanation:
The question pertains to the normal distribution and how it is represented through histograms when comparing two variables with the same mean but different variances. The normal distribution, also known as Gaussian distribution, is characterized by its bell-shaped curve, where the mean (μ) is also the median and mode of the distribution. When a variable has a lower variance, its histogram will show a taller and narrower bell curve, indicating less spread out data. Conversely, the variable with the higher variance will have a flatter and wider histogram, indicating more spread out data. Since both have the same mean, their histograms will be centered around the same point on the x-axis.
To draw the histograms for variables a (lower variance) and b (higher variance), we would start by plotting a symmetrical bell-shaped curve centered around the mean for each. The curve for a would be steeper and narrower as compared to b, which would be flatter and more spread out. The area under both curves would still sum up to one, reflecting the total probability.