Question

1. a grocery store orders 50 bags of oranges from a company’s distribution center. the bags have a mean weight of 3.85 pounds per bag. the company claims that their bags or oranges have a mean of 4 pounds. the grocery store ran a simulation of 540 bags, 2500 times, assuming a mean of 4 pounds. the results are shown below. is the mean weight of the grocery stores sample unusual? explain using the results of the simulation.

Explanation:

Step1: Identify the sample mean and population mean

The sample mean of the grocery - store's 50 bags is 3.85 pounds. The population mean claimed by the company is 4 pounds.

Step2: Analyze the simulation results

The simulation was run 2500 times with 540 bags each time assuming a mean of 4 pounds. The mean of the simulation results is 4.001 pounds.

Step3: Determine if the sample mean is unusual

If a value is more than 2 standard deviations away from the mean in a normal - distribution (a common rule - of - thumb for determining unusualness), it is considered unusual. Looking at the simulation results, the values are centered around 4 pounds. The sample mean of 3.85 pounds is relatively far from the mean of the simulation (4.001 pounds) and the claimed population mean of 4 pounds. In the simulation, values around 3.85 pounds are in the tails of the distribution, which are less common. So, the sample mean of 3.85 pounds is unusual.

Answer:

Yes, the mean weight of 3.85 pounds of the grocery store's sample is unusual. The simulation results are centered around 4.001 pounds, and 3.85 pounds is in the tail of the distribution of simulation results, indicating it is a less - common value.