Answer to Question #179347 in Statistics and Probability for Liche Kelvin

Question #179347

Chimbazeze milling company produces bags of mealie meal. The weight in Kgs per bag varies, as indicated in the below:

Weight in Kgs: 44 45 . 46 47 . 48 49 . 50

Proportion of bags: 0.04 . 0.13 0.21. 0.29. 0.20 . 0.10. 0.03

i. Compute the mean weight per bag

ii. Compute the standard deviation of the weight per bag

iii. The company estimates the cost (in ngwee) of producing a bag of mealie meal to be 752C=+Χ, where X is the number of Kgs per bag. a). Compute the mean cost of producing a bag of mealie meal.

b). Compute the standard deviation cost of producing a bag of mealie


1
Expert's answer
2021-05-03T05:53:42-0400

i. The mean is

"E[X] = \\sum x \\times P(X=x) \\\\\n\n= (44 \\times 0.04) + (45 \\times 0.13) + (46 \\times 0.21) + (47 \\times 0.29) + (48 \\times 0.20) + (49 \\times 0.10) + (50 \\times 0.03) \\\\\n\n= 1.76 + 5.86 + 9.66 + 13.63 + 9.60 + 4.90 + 1.5 \\\\\n\n= 46.91"

ii.

"E[X^2] = \\sum x^2 \\times P(X=x)\n\n= 44^2 \\times 0.04 + 45^2 \\times 0.13 + 46^2 \\times 0.21 + 47^2 \\times 0.29 + 48^2 \\times 20 + 49^2 \\times 0.10 + 50^2 \\times 0.03 \\\\\n\n= 2201.56 \\\\\n\nVar[X] = E[X^2] \u2013 (E[X])^2 \\\\\n\n= 2201.56 -46.9^2 \\\\\n\n= 1.95"

Standard deviation is

"SD[X] = \\sqrt{Var[X]} = 1.3964"

iii. Proper function C = 75 + 2X

a) The mean cost:

"E[C] = 75 + 2 \\times 46.91 = 168.82"

b) Standard deviation is

"SD[C] = \\sqrt{Var[C]} \\\\\n\n= \\sqrt{Var(75 + 2X)} \\\\\n\n= \\sqrt{2^2 \\times Var[X]} \\\\\n\n= 2 \\times SD[X] \\\\\n\n= 2 \\times 1.3964 \\\\\n\n= 2.793"


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