Final answer:
The task involves identifying the sample mean (X), population standard deviation (σ), and sample size (n) for various statistical exercises. These values are used to calculate probabilities, percentiles, and other statistical measures in a normal distribution context.
Step-by-step explanation:
The question relates to finding the mean and the standard deviation for a given frequency distribution. In the context of the given scenarios, variables such as sample mean (X), population standard deviation (σ), and sample size (n) are provided for completing various statistical calculations. When calculating probabilities and percentiles regarding the sum of the ages of individuals and the mean age for a sample, the normal distribution is utilized due to the characteristics of the underlying populations.
Examples of Key Values
- a. X = sample mean
- b. σ = population standard deviation
- c. n = sample size
For instance, with a sample mean age of 35 years, a standard deviation of 10 years, and a sample size of 39 (Try It Σ 7.6), the mean of the sum would be the sample mean multiplied by the sample size, and the standard deviation of the sum would be the population standard deviation multiplied by the square root of the sample size, assuming the distribution of the sum follows a normal distribution.