3. Describing Data Numerically

A sample of 500 random adult books in a library has an average of 312 pages with a standard deviation of 26 pages. Find the percentage of books in the sample with less than 338 pages using the Empirical Rule of Standard Deviation.

A sample of 500 random adult books in a library has an average of 312 pages with a standard deviation of 26 pages. According to the Empirical Rule of Standard Deviation, find the central range of page lengths containing 95% of the books in the sample.

The average birth weight at a hospital is 6.5lbs. with a standard deviation of 1.4lbs. What is the lowest weight which would be considered significantly high?

Salary Offers You are applying for jobs at two companies. Company C offers starting salaries with μ = $59,000 and σ = $1500. Company D offers starting salaries with μ = $59,000 and σ = $1000. From which company are you more likely to get an offer of $62,000 or more? Explain your reasoning.

Using the Empirical Rule In Exercises 29–34, use the Empirical Rule.

Use the sample statistics from Exercise 29 and assume the number of vehicles in the sample is 75.

a. Estimate the number of vehicles whose speeds are between 63 miles per hour and 71 miles per hour.

Using the Empirical Rule In Exercises 29–34, use the Empirical Rule.

The speeds for eight vehicles are listed. Using the sample statistics from Exercise 29, determine which of the data entries are unusual. Are any of the data entries very unusual? Explain your reasoning.

70, 78, 62, 71, 65, 76, 82, 64

Using Chebychev’s Theorem Old Faithful is a famous geyser at Yellowstone National Park. From a sample with n = 100, the mean interval between Old Faithful’s eruptions is 101.56 minutes and the standard deviation is 42.69 minutes. Using Chebychev’s Theorem, determine at least how many of the intervals lasted between 16.18 minutes and 186.94 minutes. (Adapted from Geyser Times)