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 $.

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Answered: 5.6-4. Approximate P(39.75 < X <…

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)

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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Question

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 $.

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