MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Transcription for Educational Website:**

The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 60 ten-gram portions of the food item is obtained and results in a sample mean of 4.5 insect fragments per ten-gram portion. Complete parts (a) through (c) below.

[Click here to view the standard normal distribution table (page 1).](#)
[Click here to view the standard normal distribution table (page 2).](#)

---

**(a) Why is the sampling distribution of \(\bar{x}\) approximately normal?**

- **A.** The sampling distribution is approximately normal because the population is normally distributed.
- **B.** The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough.
- **C.** The sampling distribution is approximately normal because the sample size is large enough.
- **D.** The sampling distribution is assumed to be approximately normal.

**Explanation:**

When we talk about the sampling distribution of the sample mean \(\bar{x}\), its shape being approximately normal often depends on the sample size and the distribution of the population. According to the Central Limit Theorem, for a sufficiently large sample size, the distribution of the sample mean will tend to be normal regardless of the population distribution.

In this particular scenario, one must consider whether the population distribution is known to be normal and if the sample size (60 in this case) is sufficient for the normal approximation.
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Transcribed Image Text:**Transcription for Educational Website:** The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 60 ten-gram portions of the food item is obtained and results in a sample mean of 4.5 insect fragments per ten-gram portion. Complete parts (a) through (c) below. [Click here to view the standard normal distribution table (page 1).](#) [Click here to view the standard normal distribution table (page 2).](#) --- **(a) Why is the sampling distribution of \(\bar{x}\) approximately normal?** - **A.** The sampling distribution is approximately normal because the population is normally distributed. - **B.** The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough. - **C.** The sampling distribution is approximately normal because the sample size is large enough. - **D.** The sampling distribution is assumed to be approximately normal. **Explanation:** When we talk about the sampling distribution of the sample mean \(\bar{x}\), its shape being approximately normal often depends on the sample size and the distribution of the population. According to the Central Limit Theorem, for a sufficiently large sample size, the distribution of the sample mean will tend to be normal regardless of the population distribution. In this particular scenario, one must consider whether the population distribution is known to be normal and if the sample size (60 in this case) is sufficient for the normal approximation.
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