The heights of the students in a statistics class are approximately normal with mean 68 inches and a standard deviation of 2.75 inches. Suppose that the heights of the 15 male students in the statistics class are also approximately normal with mean 71 inches.
Would the standard deviation for the males in the class be greater than 2.75 inches, exactly 2.75 inches, or less than 2.75 inches?
I think there is a problem here. What if there are 215 students in the stat class, 15 of which are males. The remaining 200 are female. For the statistics class, the females overwhelm the males, so the Class statistics largely reflect the females, and the males is just down in the noise. Now standard deviation: I don't see how any analysis can be done without making some assumptions about class size.
To determine whether the standard deviation for the heights of the male students in the class would be greater than, equal to, or less than 2.75 inches, we need to consider the concept of standard deviation and its relationship with the population mean and individual observations.
The standard deviation measures the spread or dispersion of a dataset. In the case of the male students' heights, if the standard deviation is greater than 2.75 inches, it implies that the heights vary more widely from the mean. Conversely, if it is less than 2.75 inches, it suggests that the heights tend to cluster closer to the mean.
In this scenario, we are given two pieces of information:
1. The heights of the entire statistics class are approximately normally distributed with a mean of 68 inches and a standard deviation of 2.75 inches.
2. The heights of the 15 male students in the class are also approximately normally distributed but have a different mean of 71 inches.
Since the heights of the male students have a different mean from the entire class, it means that the male students' heights are likely to be relatively higher than the overall class average. This implies that the male students' heights would likely deviate more from the mean compared to the entire class.
Therefore, the standard deviation for the male students' heights is expected to be greater than 2.75 inches.