Final Answer:
Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada.
a. The mean of the population is 3.35.
b. The standard deviation of the population is approximately 1.25.
c. The mean of the sample means would also be 3.35.
d. The standard deviation of the sample means would be approximately 0.28.
Step-by-step explanation:
The mean of the population (a) is calculated by summing up all the values and dividing by the total count, resulting in 3.35. To find the standard deviation of the population (b), the formula involves calculating the variance first, which measures how spread out the values are around the mean. Then, taking the square root of the variance gives the standard deviation, yielding an approximate value of 1.25, indicating the average distance of the data points from the mean.
Moving to the mean of the sample means (c), it aligns with the concept of the sampling distribution of the sample means. Given that the population mean is used as an unbiased estimator in calculating sample means, the mean of the sample means remains the same as the population mean, which is 3.35.
Regarding the standard deviation of the sample means (d), it involves the concept of standard error, indicating the variability in sample means. It's calculated by dividing the population standard deviation by the square root of the sample size. With larger sample sizes, the standard deviation of the sample means decreases. In this case, the standard deviation of the sample means is approximately 0.28, suggesting less variability among the sample means taken from this population.
Understanding these statistical measures aids in comprehending the distribution of sales figures among representatives and provides insights into the consistency and variability within the data.