Final Answer:
The x value corresponding to z = -2.25 for a population with mean (μ) = 65 and standard deviation (σ) = 4 is x = 55. The x value is calculated using the formula x = μ + (z × σ), where μ represents the mean, z denotes the z-score, and σ is the standard deviation.
Step-by-step explanation:
In statistics, the z-score represents the number of standard deviations a particular data point is from the mean of a distribution. The formula to calculate the x value from a z-score is x = μ + (z × σ), where x is the data point, μ is the mean, z is the z-score, and σ is the standard deviation.
Given that the population has a mean (μ) of 65 and a standard deviation (σ) of 4, and the z-score (z) is -2.25, substituting these values into the formula gives x = 65 + (-2.25 × 4) = 65 - 9 = 55. This means that a data point located 2.25 standard deviations below the mean in this distribution corresponds to an x value of 55.
Therefore, an x value of 55 corresponds to a z-score of -2.25 in this population. It indicates that a data point with a value of 55 is 2.25 standard deviations below the mean of 65 in this particular distribution. This method allows for the translation between z-scores and actual data values within a normal distribution, aiding in statistical analysis and interpretation of data.