Question

Downtown Artisan Butchery is butcher shop located in a medium-sized city. Jon Wembley is a butcher there. He sells meat on a commission. Over the last six months, he has sold between 50 and 70 pounds of meat a day. The amount of his sales (rounded to the nearest five pounds) and the probability of selling that much is listed in Table 1.

Table 1

Pounds sold per day	Probability of that much being sold
50	0.15
55	0.25
60	0.3
65	0.25
70	0.05

What is the expected number of pounds of meat that Jon will sell each day?

What is the variance of the amount of meat that Jon is expected to sell each day? (Do not round the expected value)

What is the standard deviation of the amount of meat that Jon is expected to sell each day? (Round to 2 decimals)

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
50	0.15	7.5	375
55	0.25	13.75	756.25
60	0.3	18	1080
65	0.25	16.25	1056.25
70	0.05	3.5	245
Sum	1	59	3512.5

Expected number is = = X * P(X) = 59

Variance = X ² * P(X) - ² = 3512.5 - 59 ² = 31.5

Standard deviation = = 5.61