Question

At a burger joint, the hourly demand of burgers show the following probability distribution. find the expected value of hourly demand and the standard deviation in hourly demand.

Number of burgers Probability

per hours

25 0.10

40 0.20

35 0.25

45 0.30

50 0.10

55 0.05

Answer 1

The expected value is calculated by the formula:

$$\mu =\sum x_iP(x_i)$$

$\mu =25\cdot0.10+40\cdot0.20+35\cdot0.25+45\cdot0.30+50\cdot0.10+55\cdot0.05=40.5$

Standard deviation is calculated by the formula:

$$\sigma=\sqrt{\sum(x_i-\mu)^2P(x_i)}$$

$(25-40.5)^2\cdot0.1+(40-40.5)^2\cdot0.2+(35-40.5)^2\cdot0.25+(45-40.5)^2\cdot0.3+(50-40.5)^2\cdot0.1+(55-40.5)^2\cdot0.05=57.25$

$\sigma = \sqrt{57.25}=7.57$

Answer:

the expected value is 40.5

the standard deviation is 7.57