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

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**Transcription for Educational Website**

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**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.

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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.
Transcribed Image Text:**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.)
Transcribed Image Text: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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