Can you help me with 3.42?

136 CHAPTER 3 | Numerical Descriptive Measures 3.40 Consider a population of 1,024 mutual funds that primarily a. Calculate the mean, variance, and standard deviation for the invest in large companies. You have determined that p, the mean population. one-year total percentage return achieved by all the funds, is 8.20 b. What proportion of these states has an average residential price and that of, the standard deviation, is 2.75. for electricity within 1 standard deviation of the mean, within a. According to the empirical rule, what percentage of these funds 2 standard deviations of the mean, and within 3 standard is expected to be within + 1 standard deviation of the mean? deviations of the mean? b. According to the empirical rule, what percentage of these funds c. Compare your findings with what would be expected based on is expected to be within 12 standard deviations of the mean? the empirical rule. Are you surprised at the results in (b)? C. According to Chebyshev's theorem, what percentage of these funds is expected to be within 1 1, 12, or + 3 standard devia- 3.43 Thirty companies comprise the DJIA. Just how big are these tions of the mean? companies? One common method for measuring the size of a com- d. According to Chebyshev's theorem, at least 93.75% of these pany is to use its market capitalization, the product of multiply- funds are expected to have one-year total returns between what ing the number of stock shares by the price of a share of stock. two amounts? On April 24, 2019, the market capitalization of these companies ranged from Traveler's $36.2 billion to Apple's $868.9 billion. 3.41 The file Cigarette Tax contains the state cigarette tax (in $) for The entire population of market capitalization values is stored in each of the 50 states and the District of Columbia as of January 1, 2019. Dow Market Cap . a. Calculate the population mean and population standard devia- Source: Data extracted from "Dow Jones Market capitalization," bit.ly/2WyJEFD. tion for the state cigarette tax. a. Calculate the mean and standard deviation of the market capi- b. Interpret the parameters in (a). talization for this population of 30 companies. SELF 3.42 The file Energy contains the average residential b. Interpret the parameters calculated in (a). TEST price for electricity in cents per kilowatt hour in each of the 50 states and the District of Columbia during a recent year. 3.5 The Covariance and the Coefficient of Correlation This section presents two measures of the relationship between two numerical variables: the covariance and the coefficient of correlation. The Covariance The covariance measures the strength of the linear relationship between two numerical variables (X and Y). Equation (3.16) defines the sample covariance, and Example 3.17 illustrates its use. SAMPLE COVARIANCE Ex - (X - n) cov(X, Y) = (3.16) n - 1 EXAMPLE 3.17 Section 2.5 uses NBA team revenue and current values stored in NBA Financial to construct a Calculating the scatter plot that showed the relationship between those two variables. Now, measure the asso- Sample Covariance ciation between the team revenue and the current value of a team by calculating the sample covariance. SOLUTION Figure 3.10 on page 137 contains the data and results worksheets that compute the covariance of revenue and value of 30 NBA teams. From the result in cell B9 of the covariance worksheet, or by using Equation (3.16) directly, you determine that the covariance is 41.3729: 1199.8133 cov(X, Y) = = 41.3729 (continued) 30 - 1