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 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?

Answer 1

Answer:

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.

$Lets\ x_1= 25\ and\ x_2= 49$

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

Formula; $z-score= \frac{x-mean}{standard\ deviation}$

z-score= $\frac{25-37}{6}$

z-score= $\frac{-12}{6} = -2$

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

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

z-score= $\frac{49-37}{6}$

z-score= $\frac{12}{6} = 2$

∴ 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= $(z-score\ x_2)- (z-score\ x_1)$

⇒ Percentage of daily phone calls numbering between 25 and 49= $(z-score\ 2)- (z-score\ -2)$

Using normal distribution table

⇒ Percentage of daily phone calls numbering between 25 and 49= $0.9772 - 0.0228= 0.9544$

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