For a population with a mean of 40 and a standard deviation of 8, find the z score corresponding to each of the following samples.

To find the z score for a sample within a population, you can use the z score formula:

z = (X – μ) / σ

Where:

• X = the value of the sample
• μ = the mean of the population
• σ = the standard deviation of the population

In this case, the population mean (μ) is 40 and the standard deviation (σ) is 8. You can apply this formula to each of the sample values (X) provided. Here’s a step-by-step explanation:

1. Subtract the population mean (40) from the sample value (X).
2. Divide the result by the population standard deviation (8).

This will give you the z score, which tells you how many standard deviations a sample value is from the mean. A positive z score indicates the sample is above the mean, while a negative z score indicates it is below the mean.

For example:

• If the sample value is 48:

z = (48 - 40) / 8 = 1.0

• If the sample value is 36:

z = (36 - 40) / 8 = -0.5

• If the sample value is 40:

z = (40 - 40) / 8 = 0

Just substitute your specific sample values into the formula to find their corresponding z scores!