**Transcription for Educational Website**---**Earthquake Interval Analysis**For earthquakes with a magnitude of 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 470 days and a standard deviation of 356 days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of 7.5 or greater on the Richter scale.1. **Calculate the Mean:** - On average, what would you expect to be the mean of the four times? - **Answer:** 470 days2. **Determine Variation Using the Three-Standard-Deviations Rule:** - How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.) - **Solution Approach:** The sample mean is expected to fall between two calculated boundaries using the standard deviation.---In this analysis, you are tasked with predicting the average interval and expected variation between significant earthquakes, using basic statistical methods. The three-standard-deviations rule helps in identifying the range within which these intervals most likely lie, based on past data. A half-century ago, the mean height of women in a particular country in their 20s was 63.4 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.84 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 25 of today's women in their 20s have mean heights of at least 64.52 inches?About ____ % of all samples have mean heights of at least 64.52 inches. (Round to one decimal place as needed.)

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Note- As per our policy we can answer only 1st question. If you want solutions for other, then you have to make a separate request. Given information Sample size = 4 Population mean µ = 470 Standard deviation σ = 356 days

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For earthquakes with a magnitude 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 470 days and a standard deviation of 356 days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of 7.5 or greater on the Richter scale. a. On average, what would you expect to be the mean of the four times? b. How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.) a. On average, what would you expect to be the mean of the four times? 470 days b. How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.) The sample mean is expected to fall between and days

For earthquakes with a magnitude 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 470 days and a standard deviation of 356 days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of 7.5 or greater on the Richter scale. a. On average, what would you expect to be the mean of the four times? b. How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.) a. On average, what would you expect to be the mean of the four times? 470 days b. How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.) The sample mean is expected to fall between and days

MATLAB: An Introduction with Applications

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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**Transcription for Educational Website**

---

**Earthquake Interval Analysis**

For earthquakes with a magnitude of 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 470 days and a standard deviation of 356 days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of 7.5 or greater on the Richter scale.

1. **Calculate the Mean:**
- On average, what would you expect to be the mean of the four times?
- **Answer:** 470 days

2. **Determine Variation Using the Three-Standard-Deviations Rule:**
- How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.)
- **Solution Approach:** The sample mean is expected to fall between two calculated boundaries using the standard deviation.

---

In this analysis, you are tasked with predicting the average interval and expected variation between significant earthquakes, using basic statistical methods. The three-standard-deviations rule helps in identifying the range within which these intervals most likely lie, based on past data.

A half-century ago, the mean height of women in a particular country in their 20s was 63.4 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.84 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 25 of today's women in their 20s have mean heights of at least 64.52 inches?

About ____ % of all samples have mean heights of at least 64.52 inches. (Round to one decimal place as needed.)

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