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AMU MATH 120 Week 5 Normal Distribution & Central Limit Theorem

Master z-scores, normal curves, and sampling distributions

Week 5 Core Topics

Week 5 introduces the normal distribution—the most important continuous probability distribution in statistics. You'll learn to find areas under the standard normal curve using z-tables, calculate probabilities for any normal distribution, convert between z-scores and x-values, and apply the Central Limit Theorem to find probabilities of sample means. This week bridges descriptive statistics and inferential statistics.

Common Week 5 Challenges

Students often struggle with z-score calculations, confusing when to add or subtract from the mean. Another challenge is reading z-tables correctly—finding area to the left, right, or between two values. The Central Limit Theorem confuses many because it requires dividing standard deviation by √n. Our materials include annotated z-tables, step-by-step z-score examples, and CLT decision flowcharts.

Week 5 Support Resources

You receive complete MyStatLab Homework 5 solutions, z-table reading guides, normal distribution calculator instructions, Central Limit Theorem practice problems, and forum posts for the Midterm Critique discussion. We provide visual aids showing when to use σ vs σ/√n and practice converting between probabilities and z-scores in both directions.

Frequently Asked Questions

❓How do I use a z-table to find probabilities?

Z-tables show the area (probability) to the LEFT of a z-score. To find area to the right, subtract the table value from 1. To find area between two z-scores, find both table values and subtract. Always draw a normal curve and shade the region you're finding to avoid errors.

❓When do I use σ vs σ/√n in normal distribution problems?

Use σ (population standard deviation) when working with individual values (X). Use σ/√n (standard error) when working with sample means (X̄). The Central Limit Theorem applies to sample means, so always divide by √n when the problem asks about averages or means of samples.

❓What is the Central Limit Theorem and why does it matter?

The Central Limit Theorem states that sample means follow a normal distribution (approximately) regardless of the population's shape, as long as sample size is large enough (usually n ≥ 30). This is crucial because it allows us to use normal distribution techniques for inference even when the population isn't normal.

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