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 9. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 28 and 46?

Answer 1

Answer:

0.6826

Step-by-step explanation:

Mean(μ) = 37

Standard deviation (σ) = 9

P(28 < x < 46) = ???

Using normal distribution

Z = (x - μ)/σ

For x = 28

Z = (28 - 37)/9

Z = -9/9

Z = -1

For x = 46

Z = (46 - 37)/9

Z = 9/9

Z = 1

We now have

P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

From the table, Z = 1 = 0.3413

φ(Z) = 0.3413

Recall that

When Z is positive, P(x<a) = 0.5 +φ(Z)

P(Z<1)= 0.5 + 0.3413

= 0.8413

When Z is negative, P(x<a) = 0.5 - φ(Z)

P(Z< -1)= 0.5 - 0.3413

= 0.1587

We now have

0.8413 - 0.1587

= 0.6826