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AP Statistics 4.1: Sampling Distribution Mean and SD

Calculate the mean and standard deviation of a sample-mean sampling distribution using the population parameters and sample size.

Syllabus
Effective Fall 2025
Course
AP Statistics

4.1.A—Calculate the mean and standard deviation of a sampling distribution of a sample mean question 1

[Maximum number: 4]

Corn tortillas are made at a large facility that produces 100,000 tortillas per day on each of its two production lines. The distribution of the diameters of the tortillas produced on production line A is approximately normal with mean 5.9 inches, and the distribution of the diameters of the tortillas produced on production line B is approximately normal with mean 6.1 inches. The figure below shows the distributions of diameters for the two production lines.

Figure for Question 4.1.A—Calculate the mean and standard deviation of a sampling distribution of a sample mean question 1 — AP Statistics

The tortillas produced at the factory are advertised as having a diameter of 6 inches. For the purpose of quality control, a sample of 200 tortillas is selected and the diameters are measured. From the sample of 200 tortillas, the manager of the facility wants to estimate the mean diameter, in inches, of the 200,000 tortillas produced on a given day. Two sampling methods have been proposed.

Method 1: Take a random sample of 200 tortillas from the 200,000 tortillas produced on a given day. Measure the diameter of each selected tortilla.

Method 2: Randomly select one of the two production lines on a given day. Take a random sample of 200 tortillas from the 100,000 tortillas produced by the selected production line. Measure the diameter of each selected tortilla.

Question (a)

(a)

For samples of size 200 taken from one day's production, describe the sampling distribution of the sample mean diameter for samples that are obtained using Method 1.

Question (b)

(b)

Suppose that one of the two sampling methods will be selected and used every day for one year ( 365 days). The sample mean of the 200 diameters will be recorded each day. Which of the two methods will result in less variability in the distribution of the 365 sample means? Explain.

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