Answer:
Step-by-step explanation:
To address this problem, let's first understand the given information and then proceed with the required calculations.
1. The distribution is roughly unimodal and symmetric.
2. The mean is 689 runs.
3. The standard deviation is 69 runs.
4. An interval one standard deviation above and below the mean is marked on the histogram.
Now, let's solve the parts (a) through (c).
a) Find the interval one standard deviation above and below the mean:
Since we are given that the standard deviation is 69 runs, we can find the interval one standard deviation above and below the mean as follows:
Lower limit = Mean - 1 * Standard Deviation
Lower limit = 689 - 69
Lower limit = 620 runs
Upper limit = Mean + 1 * Standard Deviation
Upper limit = 689 + 69
Upper limit = 758 runs
So, the interval one standard deviation above and below the mean is from 620 to 758 runs.
b) Assume the values in a bin are distributed uniformly:
Since the histogram represents the distribution of runs scored by baseball teams, and we are assuming that the values in a bin are distributed uniformly, it means that half of the values in that bin are below the line, and half are above the line. This assumption helps us understand the proportion of teams scoring within that particular range.
c) Complete the explanation for part (b):
As we have found the interval one standard deviation above and below the mean (620 to 758 runs), we can now analyze the proportion of teams scoring within this range. Since the values are uniformly distributed within a bin, we can infer that approximately half of the teams would score runs within the range of 620 to 689 runs (mean - 1 * standard deviation to the mean), and the other half would score runs within the range of 689 to 758 runs (the mean to mean + 1 * standard deviation). This information helps us understand the distribution of scores and the proportion of teams within different run-scoring ranges.
