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hoa [83]
3 years ago
11

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

ete 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?
Mathematics
1 answer:
defon3 years ago
3 0

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.

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