Question

1. for the 40 patients seen each day by a doctor’s office, the table shows the distribution of time in minutes, that it takes to complete the checkout process.

checkout time (minutes)	1	3	5	10

after the checkout desk is moved during construction, the checkout process increases by 2 minutes due to the additional walk from the exam room to the checkout desk. let ( w ) = the time, in minutes, that it takes a randomly selected patient to complete the checkout process during construction. what is the expected value of ( w )?

a) 1.425 minutes

b) 3 minutes

c) 3.425 minutes

d) 5.425 minutes

e) 21 minutes

Explanation:

Step1: Define original checkout time $X$

Let $X$ = original checkout time (minutes)

Step2: Calculate $E[X]$ (expected $X$)

$$\begin{align*} E[X] &= \frac{(1\times12)+(3\times15)+(5\times10)+(10\times3)}{40}\\ &= \frac{12 + 45 + 50 + 30}{40}\\ &= \frac{137}{40} = 3.425 \end{align*}$$

Step3: Relate $W$ to $X$

$W = X + 2$ (2 min added to all times)

Step4: Calculate $E[W]$

$$ E[W] = E[X] + 2 = 3.425 + 2 = 5.425 $$

Answer:

D) 5.425 minutes