Final answer:
The z score corresponding to a sample mean of 36 for a population with a mean of 40 and a standard deviation of 8 is -0.5. This score indicates the sample mean is half a standard deviation below the population mean.
Step-by-step explanation:
The question asks to find the z score for a sample mean of 36 when the population mean is 40 and the standard deviation is 8, for a sample size (n) of 1. The z-score formula is Z = (X - μ) / σ, where X is the sample mean, μ is the population mean, and σ is the population standard deviation.
Using the formula, we calculate:
- X = 36 (the sample mean)
- μ = 40 (the population mean)
- σ = 8 (the population standard deviation)
- Z = (X - μ) / σ = (36 - 40) / 8 = -4 / 8 = -0.5
Therefore, the z score corresponding to a sample mean of 36 is -0.5, which indicates that the sample mean is half a standard deviation below the population mean.