Question

The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. Complete parts a and b below.

Repair Calls 1 2 3 4
Probability 0.1 0.5 0.3 0.1

a. How many calls should the shop expect per hour?
b. What is the standard deviation?

Answer 1

Answer:

a) So, she can expect a 2.4 calls per hour.

b) So, the standard deviation is 0.8.

Step-by-step explanation:

We know that probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.

Repair Calls 1 2 3 4  

Probability 0.1 0.5 0.3 0.1

a) We calculate how many calls should the shop expect per hour.

We get:

$E(X)=1\cdot0.1+2\cdot0.5+3\cdot0.3+4\cdot0.1\\\\E(X)=0.1+1+0.9+0.4\\\\E(X)=2.4$

So, she can expect a 2.4 calls per hour.

b) We calculate the standard deviation:

$\sigma=\sqrt{(1-2.4)^2\cdot 0.1+(2-2.4)^2\cdot 0.5+(3-2.4)^2\cdot 0.3+(4-2.4)^2\cdot 0.1}\\\\\sigma=\sqrt{0.196+0.08+0.108+0.256}\\\\\sigma=\sqrt{0.64}\\\\\sigma=0.8$

So, the standard deviation is 0.8.