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HLT-362V Population and Sampling Distribution
The HLT-362V Population and Sampling Distribution Excel worksheet asks you to do two things: calculate Z-scores and probabilities for individual values in a normal distribution, then calculate probabilities for sample means using the standard error. You complete every calculation with Excel formulas — STANDARDIZE and NORMDIST for the normal curve, and =σ/SQRT(n) for the standard error of the mean.
The key idea the worksheet tests is that individual values spread out with the population standard deviation, while sample means spread out far less, by a factor of the square root of the sample size. This guide walks through every formula, shows a fully worked example, and explains the one concept that trips most students: the difference between a population and a sampling distribution.
What Is the Population and Sampling Distribution Worksheet?
The Population and Sampling Distribution worksheet is a Topic 2 assignment in HLT-362V Applied Statistics for Health Care that has you apply the normal distribution to both individual values and sample means in Excel. You are given a population mean and standard deviation and asked to compute Z-scores, probabilities, and sampling-distribution values.
The worksheet usually has two parts. Part A covers the population — Z-scores and probabilities for single observations. Part B covers the sampling distribution — the behavior of the average of a sample of size n.
APA formatting is not required, but your formulas must be correct and entered as live Excel functions. The assignment is graded on accuracy and on whether you used formulas rather than typing in answers.
What’s the Difference Between a Population and a Sampling Distribution?
A population distribution describes how individual values vary, while a sampling distribution describes how the average of a sample varies. They share the same center but have very different spreads.
Here is the distinction in plain terms:
- The population distribution of individual values has standard deviation σ (sigma).
- The sampling distribution of the sample mean has standard deviation σ/√n, called the standard error of the mean.
- Both are centered on the same population mean, μ.
Because you divide by the square root of n, the sampling distribution is always narrower than the population. A sample of 16 cuts the spread to one-quarter of σ; a sample of 100 cuts it to one-tenth. This narrowing is the practical meaning of the central limit theorem, a foundational result in statistics.
How Do You Calculate a Z-Score in Excel?
A Z-score measures how many standard deviations a value sits from the mean, and in Excel you calculate it with =STANDARDIZE(x, mean, standard_deviation). It is mathematically identical to =(x − mean)/standard_deviation.
For a population with mean 100 and standard deviation 8, the Z-scores are clean:
| X (value) | Z-score formula | Z |
|---|---|---|
| 84 | =STANDARDIZE(84,100,8) |
−2.00 |
| 92 | =STANDARDIZE(92,100,8) |
−1.00 |
| 108 | =STANDARDIZE(108,100,8) |
1.00 |
| 116 | =STANDARDIZE(116,100,8) |
2.00 |
A Z-score of −2 means the value 84 sits two standard deviations below the mean. Reference your mean and standard deviation as fixed cells ($B$6, $B$7) so you can copy the formula down without breaking it.
How Do You Find Normal-Distribution Probabilities in Excel?
You find the probability that a value falls below a point with =NORMDIST(x, mean, sd, 1), where the final 1 (or TRUE) returns the cumulative area under the curve. From that one function you can build every probability the worksheet asks for.
The three standard cases are:
- Less than —
P(X < 92) = NORMDIST(92,100,8,1)→ 0.1587 - Greater than —
P(X > 108) = 1 − NORMDIST(108,100,8,1)→ 0.1587 - Between two values —
P(92 ≤ X ≤ 108) = NORMDIST(108,100,8,1) − NORMDIST(92,100,8,1)→ 0.6827
That last result is the familiar 68% rule: about 68% of values fall within one standard deviation of the mean. If your between-values answer near ±1 SD lands close to 0.68, you know your formula is right.
How Do You Solve the Sampling Distribution Section?
You solve Part B by replacing the population standard deviation with the standard error of the mean, calculated as =σ/SQRT(n). Every sample-mean probability then uses that standard error in place of σ inside NORMDIST.
Follow these steps:
- Calculate the standard error:
=8/SQRT(16)= 2. - Confirm the center — the mean of the sampling distribution equals the population mean, 100.
- Compute sample-mean probabilities using the standard error as the spread:
P(x̄ < 98) = NORMDIST(98,100,2,1)→ 0.1587P(x̄ > 103) = 1 − NORMDIST(103,100,2,1)→ 0.0668P(98 ≤ x̄ ≤ 102) = NORMDIST(102,100,2,1) − NORMDIST(98,100,2,1)→ 0.6827
Notice that a sample mean above 103 has only a 6.68% chance, while an individual value above 108 had a 15.87% chance. Averaging reduces variability, which is exactly why sample means are more reliable than single measurements.
Worked Example: Mean 100, Standard Deviation 8
HLT-362V-Population-Sampling-Distribution-Example (Click to Download)
A complete worked example makes the two-part structure concrete. Using a population with μ = 100 and σ = 8, and a sample size of n = 16, the full set of answers is:
| Quantity | Result |
|---|---|
| Standard error (σ/√n) | 2.00 |
| P(X < 92) | 0.1587 |
| P(X > 108) | 0.1587 |
| P(92 ≤ X ≤ 108) | 0.6827 |
| P(x̄ < 98) | 0.1587 |
| P(x̄ > 103) | 0.0668 |
| P(98 ≤ x̄ ≤ 102) | 0.6827 |
The pattern to internalize: individual-value questions use σ = 8, sample-mean questions use the standard error = 2. Mixing these up is the single most common error on this assignment.
Which Excel Formulas Do You Need?
You only need a handful of functions to complete the entire worksheet. Keep this reference beside you:
| Task | Excel Formula |
|---|---|
| Z-score | =STANDARDIZE(x, mean, sd) |
| Probability below a value | =NORMDIST(x, mean, sd, 1) |
| Probability above a value | =1 - NORMDIST(x, mean, sd, 1) |
| Probability between two values | =NORMDIST(b, mean, sd, 1) - NORMDIST(a, mean, sd, 1) |
| Standard error of the mean | =sd / SQRT(n) |
| Sample-mean probability | =NORMDIST(value, mean, standard_error, 1) |
Note on function names: NORMDIST and STANDARDIZE work in every version of Excel and in LibreOffice. Newer Excel also offers NORM.DIST and NORM.S.DIST, which return identical results; use whichever your version recognizes.
Common Mistakes to Avoid
Most lost points on this worksheet come from a few predictable errors. Watch for these:
- Using σ instead of the standard error for sample-mean questions — the most frequent mistake.
- Forgetting the
1orTRUEinNORMDIST, which returns the curve’s height instead of a probability. - Subtracting in the wrong order for “between” probabilities (always larger minus smaller).
- Typing answers instead of formulas, which forfeits credit for showing your work.
- Confusing “greater than” with “less than” — remember
P(X > x) = 1 − NORMDIST(...).
HLT-362V Population and Sampling Distribution FAQ
What is the difference between a population and a sampling distribution?
A population distribution describes how individual values vary using the standard deviation σ, while a sampling distribution describes how sample means vary using the standard error σ/√n. Both are centered on the same mean, but the sampling distribution is always narrower.
How do I calculate standard error in Excel?
Calculate the standard error of the mean with =σ/SQRT(n), dividing the population standard deviation by the square root of the sample size. For σ = 8 and n = 16, the standard error is 8/4 = 2.
What Excel function gives normal distribution probability?
Use =NORMDIST(x, mean, sd, 1) to find the probability that a value is below x. The final argument of 1 (or TRUE) tells Excel to return the cumulative area under the normal curve.
Why is the sampling distribution narrower than the population?
The sampling distribution is narrower because its spread is the standard error, σ divided by the square root of n. Averaging multiple values cancels out extremes, so larger samples produce sample means that cluster more tightly around the population mean.
Do I use sigma or standard error for sample mean problems?
Use the standard error (σ/√n) for any question about a sample mean, and use the population standard deviation σ only for questions about individual values. Substituting the wrong spread is the most common error on this worksheet.
About the Author
This guide was prepared by the Gradevia academic team, specialists in nursing and health-sciences coursework support for students at GCU, WGU, Walden, and Liberty University. Our writers hold graduate degrees in nursing, public health, and applied statistics, and have produced hundreds of rubric-aligned HLT-362V resources covering descriptive statistics, sampling distributions, ANOVA, correlation, and article analysis. We focus on helping busy working nurses understand the method, not just the answer.
Article Update Log
- June 17, 2026 — Initial publication. Comprehensive guide to the HLT-362V Population and Sampling Distribution worksheet: Z-scores and normal-curve probabilities in Excel, the standard error of the mean, a fully worked example (μ = 100, σ = 8, n = 16), an Excel formula reference, and FAQ.
The post HLT-362V Population and Sampling Distribution: Complete Guide + Example appeared first on Your Online Resourses Guide.