Question

In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 65 and a standard deviation of 10. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 45 and 85?

Do not enter the percent symbol.
ans =  

Answer 1

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie in these ranges

So,

45 = 65 - 2 * SD

85 = 65 + 2 * SD

Remember:

In any normal distribution with mean μ and standard deviation σ : Approximately 68% of the data fall within one standard deviation of the mean. Approximately 95%of the data fall within two standard deviations of the mean. Approximately 99.7% of the data fall within three standard deviations of the mean.

So, 68.27%