Math Problem Statement

1.      If the random samples are large, what is the shape of the sampling distribution of the mean?

A.     skewed to the left                                                      C. normal

B.     skewed to the right                                                   D. rectangular

Solution

The correct answer is C. normal.

This is based on the Central Limit Theorem, which states that if random samples are sufficiently large (typically n30n \geq 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

  1. What is the Central Limit Theorem and why is it important in statistics?
  2. How does the size of the sample affect the sampling distribution of the mean?
  3. What is the relationship between the population distribution and the sampling distribution?
  4. What happens to the standard deviation of the sampling distribution as the sample size increases?
  5. Can the sampling distribution of the mean be normal for small sample sizes?

Tip: In practical applications, a sample size of 30 or more is often considered large enough for the Central Limit Theorem to apply.

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Math Problem Analysis

Mathematical Concepts

Statistics
Sampling Distribution
Central Limit Theorem

Formulas

Standard error of the mean = σ / √n

Theorems

Central Limit Theorem

Suitable Grade Level

College/University