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5.6-4. Approximate P(39.75 < X < 41.25), where X is the mean of a random sample of size 32 from a distribution with mean u = 40 and variance o2 = 8. %3D8,

5.6-4. Approximate P(39.75 < X < 41.25), where X is the mean of a random sample of size 32 from a distribution with mean u = 40 and variance o2 = 8. %3D8,

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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5.6-4

**Exercises** **5.6-1.** Let \( \bar{X} \) be the mean of a random sample of size 12 from the uniform distribution on the interval \( (0, 1) \). Approximate \( P(1/2 \leq \bar{X} \leq 2/3) \). **5.6-2.** Let \( Y = X_1 + X_2 + \cdots + X_{15} \) be the sum of a random sample of size 15 from the distribution whose pdf is \( f(x) = (3/2)x^2, -1 < x < 1 \). Using the pdf of \( Y \), we find that \( P(-0.3 \leq Y \leq 1.5) = 0.22788 \). Use the central limit theorem to approximate this probability. **5.6-3.** Let \( \bar{X} \) be the mean of a random sample of size 36 from an exponential distribution with mean 3. Approximate \( P(2.5 \leq \bar{X} \leq 4) \). **5.6-4.** Approximate \( P(39.75 \leq \bar{X} \leq 41.25) \), where \( \bar{X} \) is the mean of a random sample of size 32 from a distribution with mean \( \mu = 40 \) and variance \( \sigma^2 = 8 \).
Transcribed Image Text:**Exercises** **5.6-1.** Let \( \bar{X} \) be the mean of a random sample of size 12 from the uniform distribution on the interval \( (0, 1) \). Approximate \( P(1/2 \leq \bar{X} \leq 2/3) \). **5.6-2.** Let \( Y = X_1 + X_2 + \cdots + X_{15} \) be the sum of a random sample of size 15 from the distribution whose pdf is \( f(x) = (3/2)x^2, -1 < x < 1 \). Using the pdf of \( Y \), we find that \( P(-0.3 \leq Y \leq 1.5) = 0.22788 \). Use the central limit theorem to approximate this probability. **5.6-3.** Let \( \bar{X} \) be the mean of a random sample of size 36 from an exponential distribution with mean 3. Approximate \( P(2.5 \leq \bar{X} \leq 4) \). **5.6-4.** Approximate \( P(39.75 \leq \bar{X} \leq 41.25) \), where \( \bar{X} \) is the mean of a random sample of size 32 from a distribution with mean \( \mu = 40 \) and variance \( \sigma^2 = 8 \).
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