Weight Classification and Statistics of Bags of Rice Sold by a Food Retailer
a) What percentage of the bags weigh less than 4.5 kg?
b) If a bag is randomly selected from this shop, what is the probability that it weighs 9.0kg and 12.0kg?
c) Estimate the following statistics for the weights of the bags in this shop:
i) Modal weight
ii) Median weight
iii) Mean weight
iv) Variance
v) Standard deviation
vi) Coefficient of skewness and explain your result.
Answer:
The weight of bags of rice sold by a food retailer is classified into different categories based on weight range. Here are the statistics and calculations for the questions:
a) Percentage of Bags Weighing Less Than 4.5 kg:
To calculate the percentage of bags weighing less than 4.5 kg, we need to sum up the number of bags in the weight categories 0 to under 1.5 kg, 1.5 to under 3.0 kg, and 3.0 to under 4.5 kg. The total number of bags in these weight categories is 10 + 25 + 30 = 65. The percentage can be calculated as:
Percentage = (Number of bags weighing less than 4.5 kg / Total number of bags) * 100Percentage = (65 / 200) * 100 = 32.5%
Therefore, the percentage of bags weighing less than 4.5 kg is 32.5%.
b) Probability of Selecting a Bag Weighing Between 9.0 kg and 12.0 kg:
To calculate the probability of selecting a bag weighing between 9.0 kg and 12.0 kg, we need to find the number of bags in the weight category 9.0 to under 10.5 kg. The number of bags in this weight category is 20. The probability can be calculated as:
Probability = (Number of bags weighing between 9.0 kg and 12.0 kg / Total number of bags) * 100Probability = (20 / 200) * 100 = 10%
Therefore, the probability of selecting a bag weighing between 9.0 kg and 12.0 kg is 10%.
c) Estimated Statistics for the Weights of the Bags:
The estimated statistics for the weights of the bags in this shop are as follows:
i) Modal weight: 4.5 to under 6.0 kg
ii) Median weight: 4.5 to under 6.0 kg
iii) Mean weight: 5.175 kg
iv) Variance: 4.014 kg^2
v) Standard deviation: 2.003 kg
vi) Coefficient of skewness: 2.003
These statistics provide information about the weight distribution, central tendency, spread, and asymmetry of the weights of the bags sold by the food retailer.