True or False
A sample mean with a z-score value between 1.00 and +1.00 would be considered a fairly typical, representative sample.
True
Agree, ± 68% of the time.
True.
To determine if a sample mean with a z-score value between -1.00 and +1.00 is considered fairly typical and representative, we need to understand z-scores and their relationship to the normal distribution.
A z-score, also known as a standard score, measures the number of standard deviations a particular value is from the mean in a normal distribution. It helps us compare and understand the relative position of a value within the distribution.
In a standard normal distribution, approximately 68% of the data falls within one standard deviation of the mean, and around 95% falls within two standard deviations. This means that z-scores between -1.00 and +1.00 encompass approximately 68% of the data. Thus, a sample mean with a z-score in this range can be considered fairly typical and representative.
To calculate the z-score for a sample mean, you need to know the population mean (μ), population standard deviation (σ), sample mean (x̄), and sample size (n). Then, you can use the formula:
z = (x̄ - μ) / (σ / √n)
If the resulting z-score falls between -1.00 and +1.00, it indicates that the sample mean is within one standard deviation of the population mean, making it a fairly typical and representative sample.