BackA 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? Hint: Range Rule of Thumb - Numbers which are 2 or more standard deviations away from the mean are considered "significant".
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)
Comparing Variation in Different Data Sets In Exercises 45–50, find the coefficient of variation for each of the two data sets. Then compare the results.
Annual Salaries Sample annual salaries (in thousands of dollars) for entry level architects in Denver, CO, and Los Angeles, CA, are listed.
Mean Absolute Deviation Another useful measure of variation for a data set is the mean absolute deviation (MAD). It is calculated by the formula
MAD = Σ |x − x̄| / n.
b. Find the mean absolute deviation of the data set in Exercise 16. Compare your result with the sample standard deviation obtained in Exercise 16.
Refer to the sample statistics from Exercise 5 and determine whether any of the house prices below are unusual. Explain your reasoning.
a. \$225,000
Refer to the sample statistics from Exercise 5 and determine whether any of the house prices below are unusual. Explain your reasoning.
d. \$147,000
Temperatures It is well known that San Diego has milder weather than Chicago, but which city has more deviation from normal temperatures? Use the following data, which represent the deviation from normal high temperatures for a random sample of days. In which city would you rather be a meteorologist? Why?