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 37 and a standard deviation of 6. using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 25 and 49?

0.9544 or 95.44%

Step-by-step explanation:

Given: Mean= 37

          Standard deviation= 6

          x= 25 and 49.

Now, solving to find the percentage of daily phone calls numbering between 25 and 49.

first calculating the z-score for daily 25 phone calls.

Formula;

z-score=

z-score=

∴ z-score for daily 25 phone call is -2.

Next, calculating the z-score for daily 49 phone calls.

z-score=

z-score=

∴ z-score for daily 49 phone call is 2.

We can observe that there is change in z-score for 25 phone call and 49 phone call.

Lets use the normal distribution table to find the percentage of daily phone calls numbering between 25 and 49.

⇒ Percentage of daily phone calls numbering between 25 and 49=

⇒ Percentage of daily phone calls numbering between 25 and 49=

Using normal distribution table

⇒ Percentage of daily phone calls numbering between 25 and 49=

Hence, 0.9544 or 95.44% is the percentage of daily phone calls numbering between 25 and 49.