probability that the mean for 25 randomly selected distances is greater than 200.30 cm. the normal distribution be used in part (b), even though the sample size does not exceed 30? bability is. four decimal places as needed.) bability is four decimal places as needed.) the correct answer below. e normal distribution can be used because the finite population correction factor is small.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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### Educational Exercise: Analyzing Overhead Reach Distances

The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.6 cm.

#### Problem Set
1. **Find the probability that an individual distance is greater than 215.00 cm.**
2. **Find the probability that the mean for 25 randomly selected distances is greater than 200.30 cm.**
3. **Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?**

---

#### Solutions

**a. The probability is \[ \]**.  
*(Round to four decimal places as needed.)*

**b. The probability is \[ \]**.  
*(Round to four decimal places as needed.)*

**c. Choose the correct answer below.**

- **A.** The normal distribution can be used because the finite population correction factor is small.
- **B.** The normal distribution can be used because the probability is less than 0.5.
- **C.** The normal distribution can be used because the original population has a normal distribution.

*Correct answer: \[ \]*

---

This problem focuses on understanding how to work with normal distributions and the implications of sample size in probability calculations.
Transcribed Image Text:### Educational Exercise: Analyzing Overhead Reach Distances The overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8.6 cm. #### Problem Set 1. **Find the probability that an individual distance is greater than 215.00 cm.** 2. **Find the probability that the mean for 25 randomly selected distances is greater than 200.30 cm.** 3. **Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?** --- #### Solutions **a. The probability is \[ \]**. *(Round to four decimal places as needed.)* **b. The probability is \[ \]**. *(Round to four decimal places as needed.)* **c. Choose the correct answer below.** - **A.** The normal distribution can be used because the finite population correction factor is small. - **B.** The normal distribution can be used because the probability is less than 0.5. - **C.** The normal distribution can be used because the original population has a normal distribution. *Correct answer: \[ \]* --- This problem focuses on understanding how to work with normal distributions and the implications of sample size in probability calculations.
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