Given a population with a mean of µ = 100 and variance of o² = 81, the central limit theorem applie when the sample size is n ≥ 25. A random sample o size n = 25 is obtained. a. What are the mean and variance of the sampling distribution for the sample means? b. What is the probability that x > 102? Chapter 6 Distributions of Sample Statistics b. What is the probability that x > 109? c. What is the probability that 96 ≤ x ≤ 110? d. What is the probability that x ≤ 107?

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Given a population with a mean of m = 100 and a variance of s2 = 81, the central limit theorem applies when the sample size is n Ú 25. A random sample of size n = 25 is obtained.

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### Basic Exercises

6.5 Given a population with a mean of \( \mu = 100 \) and a variance of \( \sigma^2 = 81 \), the central limit theorem applies when the sample size is \( n \geq 25 \). A random sample of size \( n = 25 \) is obtained.

a. What are the mean and variance of the sampling distribution for the sample means?

b. What is the probability that \( \bar{x} > 102 \)?

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**Page 262**  
**Chapter 6: Distributions of Sample Statistics**

b. What is the probability that \( \bar{x} > 109 \)?

c. What is the probability that \( 96 \leq \bar{x} \leq 110 \)?

d. What is the probability that \( \bar{x} \leq 107 \)?
Transcribed Image Text:### Basic Exercises 6.5 Given a population with a mean of \( \mu = 100 \) and a variance of \( \sigma^2 = 81 \), the central limit theorem applies when the sample size is \( n \geq 25 \). A random sample of size \( n = 25 \) is obtained. a. What are the mean and variance of the sampling distribution for the sample means? b. What is the probability that \( \bar{x} > 102 \)? --- **Page 262** **Chapter 6: Distributions of Sample Statistics** b. What is the probability that \( \bar{x} > 109 \)? c. What is the probability that \( 96 \leq \bar{x} \leq 110 \)? d. What is the probability that \( \bar{x} \leq 107 \)?
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