A simple random sample of size n = 64 is obtained from a population with u = 80 and o = 32. (a) Describe the sampling distribution of x. (b) What is P (x>88)? (c) What is P (xs72)? (d) What is P (76.8

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

9

### Educational Content: Sampling Distribution

**Problem Statement:**

A simple random sample of size \( n = 64 \) is obtained from a population with a mean \( \mu = 80 \) and a standard deviation \( \sigma = 32 \).

**Questions:**

(a) **Describe the sampling distribution of \( \bar{x} \):**

(b) **What is \( P(\bar{x} > 88) \)?**

(c) **What is \( P(\bar{x} > 72) \)?**

(d) **What is \( P(76.8 < \bar{x} < 86.2) \)?**

---

**Multiple Choice:**

(a) Choose the correct description of the shape of the sampling distribution of \( \bar{x} \).

- A. The distribution is uniform.
- B. The distribution is skewed left.
- C. The distribution is skewed right.
- D. The distribution is approximately normal.
- E. The shape of the distribution is unknown.

**Explanation:**

When a simple random sample is taken and the sample size is large enough (typically \( n > 30 \)), the Central Limit Theorem suggests that the sampling distribution of the sample mean \( \bar{x} \) will be approximately normal, regardless of the shape of the population distribution. Given the sample size of 64, which is greater than 30, the correct choice for part (a) is likely:

- **D. The distribution is approximately normal.**
Transcribed Image Text:### Educational Content: Sampling Distribution **Problem Statement:** A simple random sample of size \( n = 64 \) is obtained from a population with a mean \( \mu = 80 \) and a standard deviation \( \sigma = 32 \). **Questions:** (a) **Describe the sampling distribution of \( \bar{x} \):** (b) **What is \( P(\bar{x} > 88) \)?** (c) **What is \( P(\bar{x} > 72) \)?** (d) **What is \( P(76.8 < \bar{x} < 86.2) \)?** --- **Multiple Choice:** (a) Choose the correct description of the shape of the sampling distribution of \( \bar{x} \). - A. The distribution is uniform. - B. The distribution is skewed left. - C. The distribution is skewed right. - D. The distribution is approximately normal. - E. The shape of the distribution is unknown. **Explanation:** When a simple random sample is taken and the sample size is large enough (typically \( n > 30 \)), the Central Limit Theorem suggests that the sampling distribution of the sample mean \( \bar{x} \) will be approximately normal, regardless of the shape of the population distribution. Given the sample size of 64, which is greater than 30, the correct choice for part (a) is likely: - **D. The distribution is approximately normal.**
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman