Question

The Audit Bureau of Circulations of South Africa, a nonprofit company that provides accurate and comparable circulation figures, has released newspaper-circulation statistics for the period October-December 2017. In one year, earnings growth averaged 8.2%; the standard deviation was 2.1% a. It can be guaranteed that 75% of these earnings growth will be in what interval? b. Using the empirical rule, it can be estimated that approximately 68% of these earnings growth will be in what interval? a. It can be guaranteed that 75% of these earnings growth will be in the interval up to (Simplify your answers.)

Answer 1

a. To guarantee that 75% of the earnings growth ... approximately 68% of the earnings growth will be within the interval of 6.1% to 10.3%.

Step-by-step explanation:

a. To guarantee that 75% of the earnings growth will be within a certain interval, we can use the empirical rule. Since the mean earnings growth is 8.2% and the standard deviation is 2.1%, we can calculate the interval by adding and subtracting one standard deviation from the mean. 8.2% - 2.1% = 6.1% and 8.2% + 2.1% = 10.3%. Therefore, we can guarantee that 75% of the earnings growth will be within the interval of 6.1% to 10.3%.

b. According to the empirical rule, approximately 68% of the earnings growth will be within one standard deviation of the mean. Therefore, if we add and subtract one standard deviation from the mean, the interval will be 8.2% - 2.1% = 6.1% to 8.2% + 2.1% = 10.3%. Hence, we can estimate that approximately 68% of the earnings growth will be within the interval of 6.1% to 10.3%.