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 8.5%; the standard deviation was 2.3%. a. It can be guaranteed that 84% of these earnings growth will be in what interval? b. Using the empirical rule, it can be estimated that approximately 95% of these earnings growth will be in what interval? a. It can be guaranteed that 84% of these earnings growth will be in the interval up to (Simplify your answers.)

Answer 1

The Empirical Rule is used to establish that 68% of earnings growth figures are expected between 6.2% and 10.8%, and approximately 95% are between 3.9% and 13.1%, assuming a normal distribution of data.

Step-by-step explanation:

The question pertains to statistics and the application of the Empirical Rule or the 68-95-99.7 rule in determining confidence intervals for a normally distributed dataset.

Part a

For a data distribution that is bell-shaped and symmetric, approximately 68% of the data is within one standard deviation of the mean. So, if the mean earnings growth is 8.5% and the standard deviation is 2.3%, then 68% of the earnings growth figures will fall within the interval from (8.5% - 2.3%) to (8.5% + 2.3%), which is 6.2% to 10.8%.

Part b

Using the Empirical Rule, approximately 95% of the data is within two standard deviations of the mean. So, for the earnings growth, this interval would be from (8.5% - 2*2.3%) to (8.5% + 2*2.3%), which is 3.9% to 13.1%.